Nitride based semiconductor light-emitting device

ABSTRACT

The present invention provides a semiconductor device having a semiconductor multi-layer structure which includes at least an active layer having at least a quantum well, and the active layer further including at least a luminescent layer of In x Al y Ga 1-x-y N (0&lt;x&lt;1, 0≦y≦0.2), wherein a threshold mode gain of each of the at least quantum well is not more than 12 cm −1 , and wherein a standard deviation of a microscopic fluctuation in a band gap energy of the at least luminescent layer is in the range of 75 meV to 200 meV.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a semiconductor light emittingdevice, and more particularly to a gallium nitride based semi conductorlight emitting device.

[0003] 2. Description of the Related Art

[0004] Nitride based semiconductors are extremely attractive for a bluecolor laser device. In Japan Journal Applied Physics vol. 36, 1997, pp.1568-1571, Nakamura et al. reported a continuous emission life-time forover 10,000 hours at 2 mW and at room temperature. FIG. 1 is afragmentary cross sectional elevation view of a conventional laserdiode. A GaN film 102 is formed on a sapphire substrate 101.Stripe-shaped SiO2 masks 103 are formed on the GaN film 102.

[0005] Further, a gallium nitride based multilayer structure isselectively grown by use of the stripe-shaped SiO2 masks 103, wherebythe gallium nitride based multilayer structure includes low dislocationdensity regions 104 and high dislocation density regions 116 which aremarked by hatching. The high dislocation density regions 116 can beobtained by the normal epitaxial growth in the vertical direction fromthe GaN film 102. The low dislocation density regions 104 can beobtained by the epitaxial lateral overgrowth over the stripe-shaped SiO2masks 103. A p-electrode 105 is provided on the low dislocation densityregion 104. The GaN film 102 has a high through-dislocation density.

[0006] The through-dislocations extend to the high dislocation densityregions 116 as well illustrated in the hatched region of FIG. 1. Thethrough-dislocations do not extend to the low dislocation density region104. The high dislocation density region 116 has a high dislocationdensity of not less than 1×10¹² m⁻². The low dislocation density region104 has a low dislocation density of less than 1×10¹¹ m⁻². In thevicinity of the center of the SiO2 mask 103, the epitaxial lateralovergrowths from the peripheral sides of the SiO2 mask 103 toward thecenter of the SiO2 mask 103 experience collision, whereby anotherdislocation appears, for which reason the low dislocation density region104 has another high dislocation density region over the center of theSiO2 mask 103.

[0007] The p-electrode 105 is provided on the low dislocation densityregion 104, so that a current is injected into the low dislocationdensity region 104 to avoid any deterioration of the laser device due tothe dislocation, and to obtain a possible long life-time.

[0008] Over an Si-doped n-GaN epitaxial lateral overgrowth substrate106, an Si-doped n-type In_(0.1)Ga_(0.9)N layer 107 is formed. An n-typecladding layer 108 is formed on the Si-doped n-type In_(0.1)Ga_(0.9)Nlayer 107, wherein the n-type cladding layer 108 comprises 120 periodsof Si-doped n-type GaN layers having a thickness of 2.5 nanometers, andundoped Al_(0.14)Ga_(0.86)N layers having a thickness of 2.5 nanometers.An Si-doped n-type GaN optical confinement layer 109 having a thicknessof 0.1 millimeter is formed on the n-type cladding layer 108.

[0009] A multiple quantum well active layer 110 is formed on theSi-doped n-type GaN optical confinement layer 109, wherein the multiplequantum well active layer 110 includes Si-doped n-typeIn_(0.15)Ga_(0.85)N well layers having a thickness of 3.5 nanometers andSi-doped n-type In_(0.02)Ga_(0.98)N potential barrier layers having athickness of 10.5 micrometers. An Mg-doped p-type Al_(0.2)Ga_(0.8)N caplayer 111 having a thickness of 20 nanometers is formed on the multiplequantum well active layer 110. An Mg-doped p-type GaN opticalconfinement layer 112 having a thickness of 0.1 millimeter is formed onthe Mg-doped p-type Al_(0.2)Ga_(0.8)N cap layer 111.

[0010] A p-type cladding layer 113 is formed on the Mg-doped p-type GaNoptical confinement layer 112, wherein the p-type cladding layer 113comprises 120 periods of Mg-doped p-type GaN layers having a thicknessof 2.5 nanometers, and undoped Al_(0.14)Ga_(0.86)N layers having athickness of 2.5 nanometers. An Mg-doped p-type GaN contact layer 114having a thickness of 0.05 millimeters is formed on the p-type claddinglayer 113. A dry etching process is carried out to form a ridgestructure. A p-electrode 105 and an n-electrode 115 are formed, whereinthe p-electrode 105 comprises laminations of Ni-layer and Au-layer,whilst the n-electrode 115 comprises laminations of Ti-layer andAl-layer.

[0011] In Japan journal Applied Physics vol. 36, 1997, pp. L899-902 andNEC Research and Development vol. 41, 2000, No. 1, pp. 74-85, thepresent inventors addressed that the facet-initiated epitaxial lateralovergrowth method was used to reduce the dislocation density over entireregion. In the facet-initiated epitaxial lateral overgrowth method, thestrip-shaped SiO2 masks are formed on the GaN layer over the sapphiresubstrate, and then a hydride vapor phase growth is used to cause theextending direction of the through-dislocations to be curved, wherebythe dislocation density is relaxed, no high dislocation density regionis formed. Thus, a low dislocation density n-GaN substrate can beprepared.

[0012]FIG. 2 is a fragmentary cross sectional elevation view of anotherconventional semiconductor laser device. An n-type cladding layer 122was formed on a top surface of the n-GaN substrate 121, wherein then-type cladding layer 122 comprises an Si-doped n-type Al_(0.1)Ga_(0.9)Nlayer having a silicon impurity concentration of 4×10¹⁷ cm⁻³ and athickness of 1.2 micrometers. An n-type optical confinement layer 123was formed on a top surface of the n-type cladding layer 122, whereinthe n-type optical confinement layer 123 comprises an Si-doped n-typeGaN layer having a silicon impurity concentration of 4×10¹⁷ cm⁻³ and athickness of 0.1 micrometer.

[0013] A multiple quantum well active layer 124 was formed on a topsurface of the n-type optical confinement layer 123, wherein themultiple quantum well active layer 124 comprises three In_(0.2)Ga_(0.8)Nwell layers having a thickness of 3 nanometers and Si-dopedIn_(0.05)Ga_(0.95)N potential barrier layers having a silicon impurityconcentration of 5×10¹⁸ cm⁻³ and a thickness of 5 micrometers.

[0014] A cap layer 125 was formed on a top surface of the multiplequantum well active layer 124, wherein the cap layer 125 comprises anMg-doped p-type Al_(0.2)Ga_(0.8)N layer. An optical confinement layer126 was formed on a top surface of the cap layer 125, wherein theoptical confinement layer 126 comprises an Mg-doped p-type GaN layerhaving a magnesium impurity concentration of 2×10¹⁷ cm⁻³ and a thicknessof 0.1 micrometer. A p-type cladding layer 127 was formed on a topsurface of the optical confinement layer 126, wherein the p-typecladding layer 127 comprises an Mg-doped p-type Al_(0.1)Ga_(0.9)N layerhaving a magnesium impurity concentration of 2×10¹⁷ cm⁻³ and a thicknessof 0.5 micrometers. A p-type contact layer 128 was formed on a topsurface of the p-type cladding layer 127, wherein the p-type contactlayer 128 comprises an Mg-doped p-type GaN layer having a magnesiumimpurity concentration of 2×10¹⁷ cm⁻³ and a thickness of 0.1 micrometer.

[0015] Those layers 122, 123, 124, 125, 126, 127, and 128 were formed bya low pressure metal organic vapor phase epitaxy method under a pressureof 200 hPa. A partial pressure of the ammonium gas for nitrogen sourcewas maintained at 147 hPa. TMG was used for the Ga source material. TMAwas used for the Al source material. TMI was used for the In sourcematerial. The growth temperature was maintained at 1050° C. except whenthe InGaN multiple quantum well active layer 124 was grown. In thegrowth of the InGaN multiple quantum well active layer 124, the growthtemperature was maintained at 780° C.

[0016] A dry etching process was then carried out to selectively etchthe p-type cladding layer 127 and the p-type contact layer 128 therebyforming a mesa structure 129. A silicon dioxide film 130 was formed onthe mesa structure 129 and the upper surfaces of the p-type contactlayer 128. The silicon dioxide film 130 was selectively removed from thetop surface of the mesa structure 129 by use of an exposure technique,whereby the top surface of the p-type contact layer 128 was shown and aridged structure was formed.

[0017] An n-type electrode 131 was formed on a bottom surface of thesubstrate 121, wherein the n-type electrode 131 comprises laminations ofa titanium layer and an aluminum layer. A p-type electrode 132 wasformed on a top surface of the p-type contact layer 128, wherein thep-type electrode 132 comprises laminations of a nickel layer and a goldlayer. The above structure was then cleaved to form first and secondfacets. Two samples were prepared. In the first type sample, both thefirst and second facets were then coated with a highly reflective coatof a reflectance factor of 95%, wherein the highly reflective coatcomprises laminations of titanium dioxide film and silicon dioxide film.In the second type sample, only the second facet was then coated with ahighly reflective coat of a reflectance factor of 95%, wherein thehighly reflective coat comprises laminations of titanium dioxide filmand silicon dioxide film. The first facet was uncoated. The first typesample showed a threshold current density of 1.5 kA/cm². The second typesample showed a threshold current density of 3.0 kA/cm².

[0018] For the nitride based semiconductor blue color laser device, theInGaN quantum wells are provided in the active layer. It was not easy toprepare uniform InGaN amorphous films in the crystal growth. The InGaNquantum well active layer has compositional fluctuation. In accordancewith the conventional common sense, the compositional fluctuationdeteriorates the device performances or characteristics. The issue forthe prior art was how to eliminate the compositional fluctuation.

[0019] In Applied Physics Letter vol. 71, p. 2346, 1997, Chichibu et al.reported results of considerations for the indium-compositionalfluctuation and the carrier diffusion length basd on the observation ofthe cathode luminescence image to the InGaN quantum wells. It waspresumed even the dislocation density was higher in order than theconventional one, a high luminescence efficiency could be obtainedbecause potential fluctuations of electrons and holes caused by theindium compositional fluctuation localize carriers to prevent thecarriers to be captured into the non-radiation centers. If thispresumption is correct, it may be expectable that the increase of thecompositional fluctuation without reducing the dislocation densityimproves the luminescent efficiency. Actually, however, the deviceperformances depend on the optical gain, for, which reason a variationin the state density due to the indium compositional fluctuation causesa large change in the optical gain.

[0020] In Applied Physics Letter, vol. 71, p.2608, 1997, Chow et al.addressed that the compositional fluctuation makes the gain spectrumwide, whereby the gain peak is lowered and he threshold current densityis dropped.

[0021] Japanese laid-open patent publication No. 11-340580 discloses tocontrol the indium compositional fluctuation, wherein the compositionaluniformity is improved to prevent the multi-wavelength laser emission.The compositional uniformity is measurable from the photo-luminescencepeak wavelength distribution. This publication also discloses thefollowing prior art. An InGaN non-amorphous large region is present. Asmall indium compositional region with indium index of not more than 0.2may cause a compositional isolation due to the increase in the indiumindex.

[0022] If the InGaN layer has an indium index of about 0.15, then ahalf-width of the photo-luminescence spectrum in the macroscopic scalein the order of about 200 micrometers is extremely large due tonon-uniformity of the crystal structure with the compositionalisolation, and the half-width is at least 150 meV. The publicationdiscloses, as the prior invention, that a SiC substrate is used toadjust the crystal growth rate for reducing the photo-luminescent peakwavelength distribution to about 90 meV, thereby preventing themulti-wavelength laser emission.

[0023] The above Japanese publication is silent on the important issueof further reduction of the photo-luminescent peak wavelengthdistribution from 90 meV. The effect of the indium compositionalfluctuation to the device performances had not sufficiently beclarified. The fundamental question on the compositional fluctuation ofthe InGaN quantum well in the active layer had not been outstanding.

[0024] The most attractive application of the blue color laser device isa light source for wiring and reading to the optical disks such as DVD.For the read operation, about 3 mW output of the blue color laser beamis necessary. For the write operation, about 30 mW output of the bluecolor laser beam is necessary. If the laser device is used for DVD-RAM,then the laser device should have the high output performance of about30 mW, for which reason one of the facets of the laser device is coatedwith a highly reflective coating. If the laser device is used forDVD-ROM, then the laser device should have the low output performance ofabout 3 mW, for which reason both the facets of the laser device arecoated with a highly reflective coating.

[0025] Whereas it is desired that the high output laser device shouldhave a life-time of at least 5000 hours at 30 mW and at 70° C., theactually realized life-time was at most 500 hours at 30 mW and at 60°C., which was reported by Nakamura et al. in JSAP International No. 1,pp. 5-17, 2000. The reduction in the driving current at 30 mW makes thelife-time long, for which reason it is desirable to reduce the thresholdcurrent of the high output laser.

[0026] The low output laser device may be used for the portable DVDplayer with a battery. For this low output laser device, it is desirableto reduce the low power consumption. For this purpose, it is desirableto reduce the threshold current.

[0027] In the above circumstances, the development of a novel nitridebased semiconductor light emitting device free from the above problemsis desirable.

SUMMARY OF THE INVENTION

[0028] Accordingly, it is an object of the present invention to providea novel semiconductor light emitting device free from the aboveproblems.

[0029] It is a further object of the present invention to provide anovel nitride based semiconductor light emitting device exhibiting highoutput performances with a reduced threshold current.

[0030] It is a still further object of the present invention to providea novel nitride based semiconductor light emitting device exhibiting lowoutput performances with a reduced threshold current.

[0031] It is yet a further object of the present invention to provide anovel nitride based semiconductor light emitting device emitting a bluecolor laser beam with a reduced threshold current.

[0032] The present invention provides a semiconductor device having asemiconductor multi-layer structure which includes at least an activelayer having at least a quantum well, and the active layer furtherincluding at least a luminescent layer of In_(x)Al_(y)Ga_(1-x-y)N(0<x<1, 0≦y≦0.2), wherein a threshold mode gain of each of the at leastquantum well is not more than 12 cm⁻¹, and wherein a standard deviationof a microscopic fluctuation in a band gap energy of the at leastluminescent layer is in the range of 75 meV to 200 meV.

[0033] The present invention also provides a semiconductor device havinga semiconductor multi-layer structure which includes at least an activelayer having at least a quantum well, and the active layer furtherincluding at least a luminescent layer of In_(x)Al_(y)Ga_(1-x-y)N(0<x<1, 0≦y≦0.2), wherein a threshold mode gain of each of the at leastquantum well is more than 12 cm⁻¹, and wherein a standard deviation of amicroscopic fluctuation in a band gap energy of the at least luminescentlayer is not more than of 40 meV.

[0034] The above and other objects, features and advantages of thepresent invention will be apparent from the following descriptions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Preferred embodiments according to the present invention will bedescribed in detail with reference to the accompanying drawings.

[0036]FIG. 1 is a fragmentary cross sectional elevation view of aconventional laser diode.

[0037]FIG. 2 is a fragmentary cross sectional elevation view of anotherconventional semiconductor laser device.

[0038]FIG. 3 is illustrative of an energy band gap profile of a multiplequantum well structure provided in a conventional gallium nitride basedsemiconductor laser device over sapphire substrate as the first priorart.

[0039]FIG. 4 is a diagram illustrative of calculated optical gainspectrums versus “Eph”−“Ego” at various carrier densities and at a roomtemperature (300 K) for the InGaN quantum well when the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is small, for example, equal to 3 meV, wherein “Eph” representsthe band gap energy, and “Ego” is an averaged value of the band gapenergies.

[0040]FIG. 5 is a diagram illustrative of calculated optical gainspectrums versus “Eph”−“Ego” at various carrier densities and at a roomtemperature (300 K) for the InGaN quantum well when the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is large, for example, equal to 75 meV, wherein “Eph”represents the band gap energy, and “Ego” is an averaged value of theband gap energies.

[0041]FIG. 6 is a diagram illustrative of variations of threshold modegains for one InGaN quantum well over carrier densities under conditionsof various standard deviations “σ_(g)” of the spatial variation(fluctuation) of the energy band gap, for example, 10 meV, 35 meV, 50meV, 75 meV, 150 meV, and 200 meV.

[0042]FIG. 7 is a diagram illustrative of a variation in differentialgain over the standard deviation σ_(g) of the “microscopic fluctuation”of the band gap energy profile, wherein the differential gain istheoretically calculated.

[0043]FIG. 8 is a diagram illustrative of variations in thresholdcurrent density of the laser device over the standard deviation “Eg” ofthe microscopic fluctuation of the energy band gap if both alight-emitting front facet and an opposite rear facet havehigh-reflectance coats.

[0044]FIG. 9 is a diagram illustrative of respective variations innon-radiation recombination life-time over carrier density for standarddeviations “σ_(g)” of various microscopic fluctuations from 10 meV to200 meV.

[0045]FIG. 10 is a diagram illustrative of a variation in differentialgain over the standard deviation σ_(g) of the “microscopic fluctuation”of the band gap energy profile, wherein the differential gain istheoretically calculated.

[0046]FIG. 11 is a diagram illustrative of variation in measuredphoto-luminescent life-time over temperature of the semiconductor laserdevice of FIG. 2.

[0047]FIG. 12A is a cross sectional elevation view illustrative of asemiconductor laser diode in a first example in accordance with thepresent invention.

[0048]FIG. 12B is a cross sectional elevation view illustrative of asemiconductor laser diode in a second example in accordance with thepresent invention.

[0049]FIG. 13 is a diagram illustrative of reflective spectrums whichrepresent variations in reflectance “R” over wavelength, wherein SiO₂films and TiO₂ films are alternately laminated by one pair, two pairs,three pairs and four pairs, where the SiO₂ films and TiO₂ films have athickness of 100 nanometers.

[0050]FIG. 14 is a diagram illustrative of relationships between the“macroscopic fluctuation” and “microscopic fluctuation” in the indiumcompositional profile for the first type semiconductor laser device forlow output performance in accordance with the present invention, and thefirst to third prior arts.

[0051]FIG. 15 is a diagram illustrative of relationships between the“threshold mode gain” for one quantum well and the “microscopicfluctuation” in the indium compositional profile for the first typesemiconductor laser device for low output performance in accordance withthe present invention, and the first and third prior arts.

[0052]FIG. 16 is a diagram illustrative of relationships between the“macroscopic fluctuation” and “microscopic fluctuation” in the indiumcompositional profile for the second type semiconductor laser device forhigh output performance in accordance with the present invention, andthe first to third prior arts.

[0053]FIG. 17 is a diagram illustrative of relationships between the“threshold mode gain” for one quantum well and the “microscopicfluctuation” in the indium compositional profile for the second typesemiconductor laser device for high output performance in accordancewith the present invention, and the first and third prior arts.

[0054]FIG. 18 is a photograph of the cathode luminescence image inexample 1 of the present invention.

DETAILED DESCRIPTION OF PRESENT INVENTION

[0055] A first aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of the at least quantum well is not more than 12 cm⁻¹, andwherein a standard deviation of a microscopic fluctuation in a band gapenergy of the at least luminescent layer is in the range of 75 meV to200 meV.

[0056] It is possible that a differential gain “dg/dn” of the at leastactive layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0057] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)≦12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0058] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0059] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R²” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0060] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0061] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0062] A second aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of the at least quantum well is not more than 12 cm⁻¹, andwherein a differential gain “dg/dn” of the at least active layersatisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0063] It is possible that a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer is inthe range of 75 meV to 200 meV.

[0064] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)≦12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0065] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){squareroot}(R₂)}/{(1−{square root}(R ₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0066] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0067] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0068] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. The gallium-nitride-based multi-layer structure may extend over a substrate having asurface dislocation density of less than 1×10⁸/cm².

[0069] A third aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of the at least quantum well, and wherein a standard deviation ofa microscopic fluctuation in a band gap energy of the at leastluminescent layer is in the range of 75 meV to 200 meV.

[0070] It is possible that a differential gain “dg/dn” of the at leastactive layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0071] It is also possible that a threshold mode gain of each of the atleast quantum well is not more than 12 cm⁻¹.

[0072] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){squareroot}(R₂)}/{(1−{square root}(R ₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0073] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0074] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0075] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0076] A fourth aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of the at least quantum well, and wherein a differential gain“dg/dn” of the at least active layer satisfies 0.5×10⁻²⁰(m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0077] It is possible that a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer is inthe range of 75 meV to 200 meV.

[0078] It is also possible that a threshold mode gain of each of the atleast quantum well is not more than 12 cm⁻¹.

[0079] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R ₁R₂))×({squareroot}(R₁)+{square root}(R₂))}], where “R₁” is a first reflectance of afirst cavity facet, from which a light is emitted, “R₂” is a secondreflectance of a second cavity facet opposite to the first cavity facet,“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0080] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0081] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0082] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0083] A fifth aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R₂)}/{(1−{square root} (R₁R₂))×({square root}(R₁)+{square root}(R₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to the firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of the atleast quantum well, and wherein a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer is inthe range of 75 meV to 200 meV.

[0084] It is also possible that a differential gain “dg/dn” of the atleast active layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0085] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)≦12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0086] It is also possible that a threshold mode gain of each of the atleast quantum well is not more than 12 cm⁻¹.

[0087] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0088] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0089] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over <a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0090] A sixth aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S≧3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{square root}(R₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to the firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of the atleast quantum well, and wherein a differential gain “dg/dn” of the atleast active layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).

[0091] It is also possible that a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer is inthe range of 75 meV to 200 meV.

[0092] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)≦12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0093] It is also possible that a threshold mode gain of each of the atleast quantum well is not more than 12 cm⁻¹.

[0094] It is also possible that the semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of the first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and the slope efficiency “S” satisfies S≧1.4/n (W/A).

[0095] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0096] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0097] A seventh aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of the at least quantum well is more than 12 cm⁻¹, and wherein astandard deviation of a microscopic fluctuation in a band gap energy ofthe at least luminescent layer is not more than of 40 meV.

[0098] It is possible that a differential gain “dg/dn” of the at leastactive layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).

[0099] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)>12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0100] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[({(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0101] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and loss than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0102] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0103] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0104] An eighth aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of the at least quantum well is more than 12 cm⁻¹, and wherein adifferential gain “dg/dn” of the at least active layer satisfiesdg/dn≧1.0×10⁻²⁰ (m²).

[0105] It is possible that a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer isnot more than of 40 meV.

[0106] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)>12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0107] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0108] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and less than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0109] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0110] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0111] A ninth aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of the at least quantum well, and wherein a standard deviation ofa microscopic fluctuation in a band gap energy of the at leastluminescent layer is not more than of 40 meV.

[0112] It is possible that a differential gain “dg/dn” of the at leastactive layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).

[0113] It is also possible that a threshold mode gain of each of the atleast quantum well is more than 12 cm⁻¹.

[0114] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0115] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and less than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0116] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0117] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0118] A tenth aspect of the present invention is a semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and the active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of the at least quantum well, and wherein a differential gain“dg/dn” of the at least active layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).

[0119] It is possible that a standard deviation of a microscopicfluctuation in a band gap energy of the at least luminescent layer isnot more than of 40 meV.

[0120] It is also possible that a threshold mode gain of each of the atleast quantum well is more than 12 cm⁻¹.

[0121] It is also possible that the semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{square root}(R₁R₂))×({square root}(R₁)+{squareroot}(R₂))}], where “R₁” is a first reflectance of a first cavity facet,from which a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to the first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of the at least quantum well.

[0122] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and less than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0123] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0124] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0125] An eleventh aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{squareroot}(R₁R₂))×({square root}(R₁)+{square root}(R₂))}], where “R₁” is afirst reflectance of a first cavity facet, from which a light isemitted, “R₂” is a second reflectance of a second cavity facet oppositeto the first cavity facet, “α_(m)” is a mirror loss, and “n” is a numberof the at least quantum well, and wherein a standard deviation of amicroscopic fluctuation in a band gap energy of the at least luminescentlayer is not more than of 40 meV.

[0126] It is also possible that a differential gain “dg/dn” of the atleast active layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).

[0127] It is also possible that a threshold mode gain of each of the atleast quantum well is more than 12 cm¹.

[0128] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)>12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0129] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and less than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0130] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0131] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure.

[0132] It is also possible that the gallium-nitride-based multi-layerstructure may extend over a gallium-nitride-based substrate.

[0133] It is also possible that the gallium-nitride-based multi-layerstructure may extend over a sapphire substrate.

[0134] It is also possible that the gallium-nitride-based multi-layerstructure may extend over a substrate having a surface dislocationdensity of less than 1×10⁸/cm².

[0135] A twelfth aspect of the present invention is a semiconductordevice having a semiconductor multi-layer structure which includes atleast an active layer having at least a quantum well, and the activelayer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein the semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R₂)}/{(1−{squareroot}(R₁R₂))×({square root}(R₁)+{square root}(R₂))}], where “R₁” is afirst reflectance of a first cavity facet, from which a light isemitted, “R₂” is a second reflectance of a second cavity facet oppositeto the first cavity facet, “α_(m)” is a mirror loss, and “n” is a numberof the at least quantum well, and wherein a standard deviation of amicroscopic fluctuation in a band gap energy of the at least luminescentlayer is not more than of 40 meV.

[0136] It is possible that a differential gain “dg/dn” of the at leastactive layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).

[0137] It is also possible that a threshold mode gain of each of the atleast quantum well is more than 12 cm⁻¹.

[0138] It is also possible that the semiconductor device has an internalloss “α_(i)” (cm⁻¹) which satisfies α_(i)>12×n−α_(m) (cm⁻¹), where“α_(m)” is a mirror loss, and “n” is a number of the at least quantumwell.

[0139] It is also possible that the semiconductor device has a cavitylength “L” of not less than 1000 micrometers, and the first reflectance“R₁” is not more than 20%, the second reflectance “R₂” is not less than80% and less than 100%, and the slope efficiency “S” satisfies S<2.1/n(W/A).

[0140] It is also possible that the semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.

[0141] It is also possible that the semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure. Thegallium-nitride-based multi-layer structure may extend over agallium-nitride-based substrate. The gallium-nitride-based multi-layerstructure may extend over a sapphire substrate. Thegallium-nitride-based multi-layer structure may extend over a substratehaving a surface dislocation density of less than 1×10⁸/cm².

[0142] The above first to sixth aspects of the present inventions areconcerned with the first type semiconductor light-emitting device, forexample, the first type semiconductor laser device which might besuitable for a relative low output characteristic and a relatively lowpower consumption characteristic. Various applications of the first typesemiconductor laser device might be possible. For example, if the firsttype semiconductor laser device is applied to DVD, this first typesemiconductor laser device might be suitable for read operation only.

[0143] The above seventh to twelfth aspects of the present inventionsare concerned with the second type semiconductor light-emitting device,for example, the second type semiconductor laser device which might besuitable for a relative high output characteristic. Various applicationsof the second type semiconductor laser device might be possible. Forexample, if the second type semiconductor laser device is applied toDVD, this first type semiconductor laser device might be suitable forwrite operation only.

[0144] For the above semiconductor devices of the first to twelfthaspects of the present inventions, a compositional distribution and amicroscopic fluctuation in energy band gap of the active layer areimportant parameters. Throughout the present specification, the word“fluctuation in compositional profile” means a position-dependentfluctuation possessed by a spatial distribution in compositionalprofile, which corresponds to a position-dependent variation incompositional profile.

[0145] The word “fluctuation in band gap energy” means aposition-dependent fluctuation possessed by a spatial distribution inband gap energy, which corresponds to a position-dependent variation inband gap energy. The word “microscopic fluctuation” means aposition-dependent fluctuation in a microscopic space which is definedby the sub-micron or smaller order scale which is less than 1 micrometerscale. The word “macroscopic fluctuation” means a position-dependentfluctuation in a macroscopic space which is defined by 1 micron orlarger order scale. The “macroscopic fluctuation” is measurable by amicro-photo-luminescence measurement method with a beam spot diameter ofnot less than 1 micrometer. The “microscopic fluctuation” is hard to bemeasured by the photo-luminescence measurement method with the beam spotdiameter of not less than 1 micrometer.

[0146] Further, the words “photo-luminescence layer” and “luminescentlayer” mean the layer which is included in the active layer and whichallows an inverted population, thereby to generate a certain gain. Ifthe active layer comprises a quantum well structure, one or more quantumwell layers correspond to the luminescent layers. If the active layerhas a multiple quantum well structure, than the fluctuation means afluctuation existing in all quantum well layers. If the active layer isfree of the quantum well structure, then the active layer mightgenerally correspond to the luminescent layer.

[0147] The “micro-fluctuation” in the sub-micron or smaller order scaleis important for the present invention. In accordance with theconventional common sense, since the conventional gallium nitride laserdiode has the InGaN active layer which include many dislocations, it isconsidered that an indium-compositional fluctuation is desirable forobtaining good laser performances.

[0148] Contrary to the conventional common sense, in accordance with thepresent invention, it is important that the surface dislocation densityof the base layer or the surface dislocation density of the bottomsurface of the active layer is reduced as many as possible and furtherthat both the micro-fluctuations in the composition and the band gapenergy of the luminescent layer in the active layer are controlledwithin predetermined individual levels as defined above so as to keepboth the high photo-luminescent efficiency and the desirable laserthreshold value and further to realize the possible long life-time ofthe laser device.

[0149] There are two main reasons for deteriorating the semiconductorlaser device. One is the deterioration of the facet. Another is theincrease in the defects of the active layer. The facet deterioration isalso so called to as impact deterioration, wherein the current laseremission is instantaneously discontinued. The increase in the defects ofthe active layer is gentle and not instantaneous, for which reason theoperating current is gradually decreased. It was already confirmed thatthe conventional laser diode shown in FIG. 1 shows a gradual decrease inthe operating current due to the gradual increase the defects of theactive layer. In order to realize the long life-time of the device, itis effective to prevent the increase the defects of the active layer.

[0150] The fluctuations in the compositions and in the band gap energyof the active layer might generate local strains in the active layer.Those local strains cause defects in the active layer upon receipt ofenergy from heat, photons and carriers in the device operation at a hightemperature. The present inventors considered that in order to realizethe life-time of the device, it is effective to reduce the fluctuationsin the compositional profile and band gap energy profile of the activelayer.

[0151] Each of the fluctuations in the compositional profile and theband gap energy profile of the active layer are classified into twotypes, first one is the “macroscopic fluctuation” in the macroscopicscale, and second one is the “microscopic fluctuation” in themicroscopic scale. The “macroscopic fluctuation” means the fluctuationin the scale which is measurable by the micro-photo-luminescencemeasurement with a beam spot diameter of not less than 1 micrometer,wherein the “microscopic fluctuation” is represented by a measuredphoto-luminescence peak wavelength distribution.

[0152] The photo-luminescence peak wavelength distribution is rangedfrom a maximum value to a minimum value of the measuredphoto-luminescence peak wavelength. In the prior art common sense, thefluctuation generally means the “macroscopic fluctuation” which ismeasurable by the photo-luminescence measurement, namely the fluctuationin the 1-micrometer order scale because the micro-photo-luminescencemeasurement is made with the beam spot diameter of not less than 1micrometer. In Japanese laid-open patent publication No. 11-340580, thedescribed fluctuation is the “macroscopic fluctuation” in themacroscopic scale, and this prior art was to reduce the “macroscopicfluctuation” for preventing laser emission in multiple wavelength.

[0153] The present invention focus on the fluctuation in the shorter orsmaller scale than “macroscopic fluctuation” in the above conventionalcommon sense. The present invention focus on the “microscopicfluctuation” in the microscopic scale which is shorter than the carrierdiffusion length, for example, approximately 1 micrometers. inaccordance with the present invention, the “microscopic fluctuation” isof the sub-micron order scale, typically 500 nanometers or less. Thepresent invention intends to control the “microscopic fluctuation” forcontrolling the local strains in the active layer including theluminescent layer in order to realize the long life-time of thesemiconductor laser diode.

[0154] In Japanese laid-open patent publication No. 11-340580, it ismentioned to reduce the fluctuation in the macroscopic scale forcontrolling the laser emission in multiple wavelengths. The reduction inthe fluctuation in the macroscopic scale does not realize the longlife-time of the device in the operation at high temperature for thereasons which will be described below in the embodiments.

[0155] The present invention is to reduce the “microscopic fluctuations”in the compositional profile and the band gap energy profile of theactive layer in the microscopic scale which is immeasurable by themicro-photo-luminescence measurement, whereby the long life-time of thedevice in the operation at high temperature is realized.

[0156] In the past, there had been no investigation on control of the“microscopic fluctuations” in the microscopic scale nor report about anyinfluence of the “microscopic fluctuations” to the device performances,There had not been known any certain or available method of how toreduce the “microscopic fluctuations” in the microscopic scale. Asdisclosed in Japanese laid-open patent publication No. 11-340580, it hadbeen known that the “macroscopic fluctuations” in the macroscopic scaleis reducible by reducing the dislocation density of the substrate andadjusting the growth rate of the active layer. The reductions of the,“microscopic fluctuations” are not obtained by those conventionalmethods.

[0157] The present invention was established by drawing the attention tothe “microscopic fluctuations” which had never been considered in theprior art. The present invention was realized by the reductions in the“microscopic fluctuations” in the compositional profile and the band gapenergy profile of the active layer in the microscopic scale, and also bykeeping a desirable high differential gain if the semiconductor deviceis applied to the laser diode. Those reductions in the “microscopicfluctuations” provide the effects that the local strain in theluminescent layer included in the active layer is controlled to reduce athreshold current of the laser.

[0158] The “microscopic fluctuation” of the threshold mode gain valuefor one of the quantum wells and the “microscopic fluctuation” of theinternal loss are important factors for the present invention. Forapplication to the first type semiconductor light emitting device withthe low output performance, it is preferable that the threshold modegain value is not more than a predetermined value, and the “microscopicfluctuation” thereof is within a predetermined range. For application tothe second type semiconductor light emitting device with the high outputperformance, it is preferable that the threshold mode gain value is notless than a predetermined value, and the “microscopic fluctuation”thereof is within a predetermined range.

[0159] The first type semiconductor light emitting device of the presentinvention shows low output performances and low power consumption, forwhich reasons the first type semiconductor light emitting device mightbe suitable for the light source for optical disk. The followingdescriptions will focus on the reason why the threshold current densitymay be reduced.

[0160] The present inventors conducted the study in the theoreticalviewpoints to have confirmed how “compositional fluctuation” of theactive layer having one or more InGaN quantum wells influence to thethreshold current density. It was assumed that a spatial variation(fluctuation) of the band gap due to the indium-compositionalfluctuation would have the normal distribution, and the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap would be an index for the “compositional fluctuation”.

[0161] In correspondence with this, it was also assumed that spatialdistributions of electrons and holes depend on a band off-set ratio of3:7. Both the electrons and holes have parabolic distributionrelationships. State densities for electrons and holes were calculatedrespectively, provided that an energy band of a quantum state of “n=1”was considered for electrons, and an energy band of a quantum state of“n=1” was considered for A-band and B-band for holes. If no fluctuationis present, the state densities of the quantum wells are given by sharpstep-functions with rapid rising. If a certain fluctuation is present,the state densities of the quantum wells are given by error-functionswith gentle rising. The use of quantized state densities for holes andelectrons allows calculations of optical gain characteristics for thevarious quantum wells with various compositional fluctuations.

[0162] The present inventors calculated the optical gains, assumed thatcarriers, for example, holes and electrons in current injections havespatially uniform Fermi energies. This assumption was made inconsideration of a spatial scale of the compositional fluctuation. Theassumption that in the current injection, the Fermi energies would bespatially uniform means that the spatial scale of the compositionalfluctuation is smaller than the diffusion lengths of the carriers, forexample, electrons and holes. If the diffusion length of the carriers isabout 1 millimeter, the spatial scale of the compositional fluctuationis not larger than the sub-micron order.

[0163] In Applied Physics Letter vol. 71, p-2346, 1997, Chichibu et al.reported that the scale of the indium-compositional fluctuation of theInGaN quantum wells observed by a cathode luminescence measurementmethod is about a several tends nanometers to a few hundreds nanometers.This report supports that the above assumptions made by the presentinventors would be reasonable.

[0164]FIG. 4 is a diagram illustrative of calculated optical gainspectrums versus “Eph”−“Ego” at various carrier densities and at a roomtemperature (300 K) for the InGaN quantum well when the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is small, for example, equal to 3 meV, wherein “Eph” representsthe band gap energy, and “Ego” is an averaged value of the band gapenergies.

[0165]FIG. 5 is a diagram illustrative of calculated optical gainspectrums versus “Eph”−“Ego” at various carrier densities and at a roomtemperature (300 K) for the InGaN quantum well when the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is large, for example, equal to 75 meV, wherein “Eph”represents the band gap energy, and “Ego” is an averaged value of theband gap energies.

[0166] For FIGS. 4 and 5, a dotted narrow line represents a calculatedoptical gain spectrum at a carrier density of 3×10¹⁵ cm⁻³. A continuousnarrow line represents another calculated optical gain spectrum at acarrier density of 3×10¹⁸ cm⁻³. A broken broad line represents stillanother calculated optical gain spectrum at a carrier density of 1×10¹⁹cm⁻³. A dotted broad line represents yet another calculated optical gainspectrum at a carrier density of 2×10¹⁹ cm⁻³. A continuous broad linerepresents yet another calculated optical gain spectrum at a carrierdensity of 3×10¹⁹ cm⁻³.

[0167] As shown in FIG. 4, when the carrier density is 3×10¹⁵ cm⁻³represented by the dotted narrow line, no optical gain is generatedunder the low standard deviation “σ_(g)” equal to 3 meV; where no dottednarrow line appears in FIG. 4. If the standard deviation “σ_(g)” of thespatial variation (fluctuation) of the energy band gap is small, then alight-transparent carrier density is relatively large. As the carrierdensity increases up to 3×10¹⁹ cm⁻³, abrupt or rapid increase in thestate density is caused to obtain a narrow and sharp-peaked gainspectrum and a large differential gain. The sharp-peak points of thegain spectrums are slightly shifted toward a high energy side andrapidly and greatly shifted toward a high gain side when increasing thecarrier density.

[0168] By contrast, as shown in FIG. 5, when the carrier density is3×10¹⁵ cm⁻³ represented by the dotted narrow line, a certain opticalgain is generated under the high standard deviation “σ_(g)” equal to 75meV, where a dotted narrow line appears in FIG. 5. If the standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is large, then carriers are flown into the potential valleysprovided by the potential fluctuations, whereby the carriers arelocalized and concentrated in the potential valleys. This causesinverted populations in localized areas corresponding to the potentialvalleys.

[0169] The optical gain is caused in a localized state which is a lowerenergy side than the averaged band gap energy “Ego” which corresponds to0.0 of “Eph”−“Ego”. The inverted population is caused to generate theoptical gain in the spatially localized relatively narrow region. In theother region free of any inverted population, no absorption loss iscaused, for which reason the other region is transparent to the light.Even the optical gain is in fact caused in the localized region, thisoptical gain may be observed as a certain gain value in total on theentire regions. In this case, the optical gain is quickly saturated.

[0170] As the carrier density increases up to 3×10¹⁹ cm⁻³, gentleincrease in the state density is caused to obtain a wide andgently-peaked gain spectrum and a small differential gain. Thegently-peak points of the gain spectrums are largely shifted toward thehigh energy side and gently shifted toward the high gain side whenincreasing the carrier density.

[0171]FIG. 6 is a diagram illustrative of variations of threshold modegains for one InGaN quantum well over carrier densities under conditionsof various standard deviations “σ_(g)” of the spatial variation(fluctuation) of the energy band gap, for example, 10 meV 35 meV, 50meV, 75 meV, 150 meV, and 200 meV. As described above, the large spatialvariation (fluctuation) of the energy band gap is advantageous inreducing the transparent carrier density, but disadvantageous inreducing the differential gain. An issue is now raised of whether thepresence of the fluctuation of the energy band gap would be advantageousor disadvantageous in view of the threshold carrier density. This issue,however, depends on the threshold mode gain for one quantum well.

[0172] If the threshold mode gain for one quantum well is less than 12cm⁻¹, the increase from 10 meV to 200 meV of the standard deviations“σ_(g)” of the spatial variation (fluctuation) of the energy band gapdecreases the threshold carrier density. Namely, the large standarddeviation “σ_(g)” of the spatial variation (fluctuation) of the energyband gap is advantageous. By contrast, if the threshold mode gain forone quantum well is more than 12 cm⁻¹, the decrease from 200 meV to 10meV of the standard deviations “σ_(g)” of the spatial variation(fluctuation) of the energy band gap decreases the threshold carrierdensity.

[0173] Namely, the small standard deviation “σ_(g)” a gel of the spatialvariation (fluctuation) of the energy band gap is advantageous. Thethreshold mode gain for one quantum well depends on the internal loss,the reflectances of the cavity and the number of the quantum wells. Theissue of advantage or disadvantage of the indium compositionalfluctuation depends on those parameters in design of the laser device.

[0174] As described above, the indium compositional fluctuation isadvantageous in reducing the transparent carrier density, butdisadvantageous in reducing the differential gain. The advantage ordisadvantage of the indium compositional fluctuation depends thethreshold mode gain for one quantum well. The preferable degrees of theindium compositional fluctuation depend on the threshold mode gain forone quantum well.

[0175] In Applied Physics Letters, vol. 71, p. 2608, 1997, Chow et alreported a theoretical estimation on the effect of the indiumcompositional fluctuation to the characteristics or performances of thelaser diode, however, provided that the indium compositional fluctuationmakes the gain spectrum wide. They were silent on the important factsthat the indium compositional fluctuation contributes to reduce thetransparent carrier density. They addressed that the indiumcompositional fluctuation is the undesirable factor for providing theundesirable influence to the laser diode.

[0176] Under the condition that the indium-compositional fluctuation isthe “macroscopic fluctuation” or the spatial scale of the compositionalfluctuation is more than micron order, it is theoretically not inherentor not nature that the carriers are flown into the potential valleysprovided by the potential fluctuations, and are localized andconcentrated in the potential valleys, thereby causing invertedpopulations in localized areas corresponding to the potential valleys.

[0177] Under the different condition that the indium-compositionalfluctuation is the “microscopic fluctuation” or the spatial scale of thecompositional fluctuation is in the sub-micron order or smaller ordereven no compositional macroscopic fluctuation in the micron order orlarger order is present, it is theoretically just inherent or naturethat the carriers are flown into the potential valleys provided by thepotential fluctuations, and are localized and concentrated in thepotential valleys, thereby causing inverted populations in localizedareas corresponding to the potential valleys. The compositional“microscopic fluctuation” contributes to improve the characteristic ofthe laser diode. Throughout the specification, the “compositionalfluctuation” associated with the present invention is the “microscopicfluctuation” or the spatial variation in composition in the sub-micronorder scale or small scale.

[0178]FIG. 7 is a diagram illustrative of variations in thresholdcurrent density of the laser device over the standard deviation “Eg” ofthe microscopic fluctuation of the energy band gap if only a rear facet,which is opposite to a light-emitting front facet, has ahigh-reflectance coat. FIG. 8 is a diagram illustrative of variations inthreshold current density of the laser device over the standarddeviation “Eg” of the microscopic fluctuation of the energy band gap ifboth a light-emitting front facet and an opposite rear facet havehigh-reflectance coats.

[0179] In both FIGS. 7 and 8, the dependencies of the threshold currentdensities on the standard deviation “Eg” of the microscopic fluctuationof the energy band gap were calculated under the conditions that thenumber of the quantum wells is 3, and the internal loss is 15 cm⁻¹. InFIG. 7, the mirror loss is 20 cm⁻¹. In FIG. 8, the mirror loss is 1cm⁻¹. The laser device of FIG. 7 will hereinafter be referred to as asingle facet HR-coated laser device. The laser device of FIG. 8 willhereinafter be referred to as both facets HR-coated laser device. It isassumed that an optical confinement coefficient is 1% for the singlequantum well. For the single facet HR-coated laser device of FIG. 7, thethreshold mode gain for the single quantum well is about 14 cm⁻¹. Forthe both facets HR-coated laser device of FIG. 8, the threshold modegain for the single quantum well is about 6 cm⁻¹.

[0180] As shown in FIG. 7, as the standard deviation “Eg” of themicroscopic fluctuation of the energy band gap becomes large, thethreshold current density simply increases. As the standard deviation“Eg” of the microscopic fluctuation of the energy band gap is small,then the threshold current density is also small. As the standarddeviation “Eg” of the microscopic fluctuation of the energy band gap isnot more than 40 meV, then a remarkable effect of reduction in thethreshold current density of the single facet HR-coated laser device canbe obtained.

[0181] As shown in FIG. 8, as the standard deviation “Eg” of themicroscopic fluctuation of the energy band gap increases up to 75 meV,the threshold current density simply decreases. As the standarddeviation “Eg” of the microscopic fluctuation of the energy band gapincreases from 75 meV up to 200 meV, the threshold current densityremains low and not more than 1 kA/cm². As the standard deviation “Eg”of the microscopic fluctuation of the energy band gap is in the range of75 meV to 200 meV, then a remarkable effect of reduction in thethreshold current density of the both facets HR-coated laser device canbe obtained.

[0182] Under other conditions than described above and shown in FIGS. 7and 8, it was shown, even illustrations are omitted, that if thethreshold mode gain for the single quantum well is more than 12 cm⁻¹,the control of the standard deviation “Eg” to less than 40 meV of themicroscopic fluctuation of the energy band gap reduces the thresholdcurrent density, whilst if the threshold mode gain for the singlequantum well is less than 12 cm⁻¹, the control of the standard deviation“Eg” into the range of 75 meV to 200 meV of the microscopic fluctuationof the energy band gap reduces the threshold current density.

[0183] The threshold current density is proportional to the thresholdcarrier density. If the threshold mode gain for the single quantum wellis more than 12 cm⁻¹, the control of the standard deviation “Eg” to lessthan 40 meV of the microscopic fluctuation of the energy band gapreduces the threshold carrier density. If the threshold mode gain forthe single quantum well is less than 12 cm⁻¹, the control of thestandard deviation “Eg” into the range of 75 meV to 200 meV of themicroscopic fluctuation of the energy band gap reduces the thresholdcarrier density.

[0184] The above descriptions have been made based on the generallycorrect assumption that the threshold carrier density has the one-to-onecorrespondence to the threshold current density. In more precisely, itis not perfectly correct assumption that the threshold carrier densityhas the one-to-one correspondence to the threshold current density. Inmore precisely, it is the perfectly correct assumption that thethreshold current density is proportional to [(the threshold carrierdensity)/(the carrier recombination life-time)]. Namely, the thresholdcurrent density depends on not only the threshold carrier density butalso the carrier recombination life-time.

[0185] The following descriptions will be made under the perfectlycorrect assumption that the threshold current density is proportional to[(the threshold carrier density)/(the carrier recombination life-time)].In case of nitride based semiconductor, the carrier recombinationlife-time may correspond mainly to the non-radiation recombinationlife-time. The increase of the non-radiation recombination life-timemakes the carrier recombination life-time increase, thereby reducing thethreshold current density.

[0186] Carriers are captured by valley portions of the “microscopicfluctuation” of the potential energy or the energy band gap, wherein the“microscopic fluctuation” of the potential energy or the band gap energyis provided by the “microscopic fluctuation” of the indium compositionprofile. The captured carriers in the valley portions are controlled tofreely move from the valley portions over the potential barriers. Thismeans that the probability of capturing the carriers into the defects ornon-radiation centers is low, whereby the non-radiation recombinationlife-time is long. If, however, the carrier density increases even thefluctuation is large, the potential valleys are filled up with thecarriers and excess carriers are over-flown from the potential valleys.The over-flown carriers are free to move, whereby the probability ofcapturing the carriers into the defects or non-radiation centers becomeshigh, whereby the non-radiation recombination life-time becomes short.

[0187]FIG. 9 is a diagram illustrative of respective variations innon-radiation recombination life-time over carrier density for standarddeviations “σ_(g)” A of various microscopic fluctuations from 10 meV to200 meV. In the range of the standard deviations “σ_(g)” of variousmicroscopic fluctuation from 75 meV to 200 meV, if the carrier densityis less than 1.5×10¹⁹ cm⁻³, the non-radiation recombination life-time islong. With reference again to FIG. 6, if the threshold mode gain is notmore than 8 cm⁻¹ and if the standard deviations “σ_(g)” of variousmicroscopic fluctuation is in the range from 75 meV to 200 meV, then thecarrier density is not more than 1.5×10¹⁹ cm⁻³.

[0188] Accordingly, if the threshold mode gain for the single quantumwell is not more than 12 cm⁻¹, the reduction of the threshold carrierdensity reduces the threshold current density. If the threshold modegain for the single quantum well is not more than 8 cm⁻¹, an additionaleffect of increase in the carrier recombination life-time furthercontributes to reduce the threshold current density, whereby aremarkable reduction of the threshold current density can be obtained.

[0189] An inter-relationship between the threshold mode gain for thesingle quantum well and the structure of the laser device will bedescribed, The threshold mode gain corresponds to the sum of theinternal loss and the mirror loss. For the InGaN-based laser diode, theoptical confinement coefficient for the single quantum well may beestimated about 1%. If the threshold mode gain of the single quantumwell is larger than 12 cm⁻¹, the internal loss “α_(i)” satisfies:

α_(i)>12×n−α _(m) (cm⁻¹)

[0190] where “α_(m)” is a mirror loss, and “n” is the number of thequantum wells.

[0191] If the threshold mode gain of the single quantum well is equal toor smaller than 12 cm⁻¹, the internal loss “α_(i)” satisfies:

α_(i)≦12×n−α _(m) (cm⁻¹).

[0192] If the threshold mode gain of the single quantum well is equal toor smaller than 8 cm⁻¹, the internal loss “α_(i)” satisfies:

α_(i)≦8×n−α _(m) (cm⁻¹).

[0193] The threshold mode gain for the single quantum well may be linkedthrough the internal loss to the slope efficiency. For the semiconductorlaser diode emitting a light having a wavelength of 400 nanometers, atheoretical limitation of the slope efficiency is 3 (W/A). The actualslope efficiency is the product of 3 and a predetermined factor. Theactual slope efficiency is given by:

S=3×{α_(m)/(α_(i)+α_(m))}×[{(1−R ₁){square root}(R ₂)}/{(1−{squareroot}(R ₁ R ₂))×({square root}(R ₁)+{square root}(R ₂))}],

[0194] where “R₁” is a first reflectance of a first cavity facet, fromwhich a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to said first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of said at least quantum well.

[0195] The above equation: α_(i)>12×n−α_(m) is incorporated into theabove equation for the slope efficiency. The following equation isobtained.

S<3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root} (R ₁)+{square root}(R ₂))}].

[0196] If the cavity length is not more than 1 millimeter, S<2.1/n W/A).

[0197] From α_(i)≦12×n α_(m) (cm⁻¹), the following equation can beintroduced.

S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}].

[0198] If the cavity length is not more than 200 millimeter, S≧1.4/n(W/A).

[0199] The standard deviation of the microscopic fluctuation of the bandgap energy may be converted to the standard deviation of the microscopicfluctuation of the indium composition or the standard deviation of themicroscopic fluctuation of the differential gain. An inter-relationshipbetween the standard deviation “Δ_(x)” in the “microscopic fluctuation”of the indium composition of In_(x)Ga_(1-x)N and the standard deviation“σ_(g)” in the “microscopic fluctuation” of the energy band gap ofIn_(x)Ga_(1-x)N will be described. In Journal of Applied Physics vol.46, p. 3432, 1975, Osamura et al. reported that the band gap energy “Eg”is given by:

Eg=3.40(1−x)+2.07x−1.0x(1−x) (eV)

[0200] If In_(x)Ga_(1-x)N is used for the active layer of a blue colorlaser diode, then x=approximately 0.15:x=approximately 0.1 toapproximately 0.3. Under this condition, dE/dx=0.6 (eV). Thus, theinterrelationship between the standard deviation “Δ_(x)” and thestandard deviation “σ_(g)” is given by:

Δ_(x)=σ_(g)/0.6 (eV)

[0201] What the standard deviation “σ_(g)” in the “microscopicfluctuation” of the energy band gap is not more than 40 meV means thatthe standard deviation “Δ_(x)” in the “microscopic fluctuation” of theindium composition is not more than 0.067. What the standard deviation“σ_(g)” in the “microscopic fluctuation” of the energy band gap is inthe range of 75 meV to 200 meV means that the standard deviation “Δ_(x)”in the “microscopic fluctuation” of the indium composition is in therange of 0.125 to 0.333.

[0202] The above descriptions are commonly applicable to the devicehaving the photo-luminescence layer of In_(x)Al_(y)Ga_(1-x-y)N (0<x<1,0≦y≦0.2). Notwithstanding, it is particularly preferable that thephoto-luminescence layer has a composition of In_(x)Al_(y)Ga_(1-x-y)N(0<x≦0.3, 0≦y≦0.05) or another composition of In_(x)Ga_(1-x)N (0<x≦0.3).

[0203] Further, the description will focus on the relationship betweenthe standard deviation σ of the “microscopic fluctuation” of the bandgap energy profile of In_(x)Ga_(1-x)N and the differential gain of thelaser device. Each of the “microscopic fluctuation” of the band gapenergy profile and the “microscopic fluctuation” of the indiumcompositional profile has an inter-relationship with the differentialgain.

[0204]FIG. 10 is a diagram illustrative of a variation in differentialgain over the standard deviation σ_(g) of the “microscopic fluctuation”of the band gap energy profile, wherein the differential gain istheoretically calculated. As the standard deviation σ_(g) of the“microscopic fluctuation” of the band gap energy profile is increased,then the differential gain is decreased. If the “microscopicfluctuation” of the band gap energy profile is large, then the densityof state at the band edge is gently risen, whereby the gain saturationby the carrier injection is likely to be caused. As a result, a smalldifferential gain is obtained. By contrast, if the “microscopicfluctuation” of the band gap energy profile is small, then the densityof state of the step function based on the two-dimensionality of thequantum well is effective, whereby a large differential gain isobtained.

[0205] In FIG. 10, if the standard deviation σ_(g) of the “microscopicfluctuation” of the band gap energy profile is 40 meV, then thedifferential gain is 1.0×10⁻²⁰ m² (1.0×10⁻¹⁶ cm²). If the standarddeviation σ_(g) of the “microscopic fluctuation” of the band gap energyprofile is not more than 40 meV, then this means that the differentialgain is not less than 1.0×10⁻²⁰ m². If the standard deviation σ_(g) ofthe “microscopic fluctuation” of the band gap energy profile is in therange of 75 meV to 200 meV, then this means that the differential gainis in the range of 0.5×10⁻²⁰ m² to 0.7×10⁻²⁰ m².

[0206] The descriptions will then focus on relationships of the presentinvention from the above decried first, second and third prior arts. Thefirst prior art is disclosed in IEEE Journal Of Selected Topics InQuantum Electronics vol. 3, No. 3, June 1997. The second and third priorarts are disclosed in Japanese laid-open patent publication No.11-340580.

[0207] In accordance with the present invention, a gallium nitride basedmaterial or sapphire is preferably selected for the substrate materialfor the purpose of defining the compositional profile of the activelayer and defining the fluctuation of the band gap energy of the activelayer It is of course possible that silicon carbide is selected for thesubstrate material. This selection makes not easy to adjust the“microscopic fluctuation” of the compositional profile of the activelayer.

[0208] Sapphire is larger in thermal, expansion coefficient than thegallium nitride based materials. The gallium nitride based materials arelarger in thermal expansion coefficient than silicon carbide. After thegallium nitride based semiconductor layer is formed over the siliconcarbide substrate, then a cooling process is carried out, wherebytensile strains reside in the gallium nitride based semiconductor layerin a plan parallel to the surface of the substrate. If the siliconcarbide substrate is used for the semiconductor laser device, then thetensile thermal strain resides in the active layer. The residual tensilestrain makes it difficult to stably adjust the compositional fluctuationparticularly the compositional microscopic fluctuation, If the sapphiresubstrate is used for the semiconductor laser device, then only thecompressive thermal strain resides in the gallium nitride basedsemiconductor layer in a plane parallel to the surface of the substrate.The semiconductor layer has a higher strength against the compressivestrain than the tensile strain. Thus, it is relatively easy to stablyadjust the compositional fluctuation. If GaN or AlGaN is selected forthe substrate material, then the gallium nitride based semiconductorlayer is similar in thermal expansion coefficient to the GaN or AlGaNsubstrate, for which reason almost no residual thermal strain is presentin the gallium nitride based semiconductor layer. It is, therefore, easyto stably adjust the compositional fluctuation particularly themicroscopic compositional fluctuation. For the above reasons, it ispreferable to select gallium nitride based materials or sapphire for thesubstrate material.

[0209] The present invention will be compared with the prior arts inview of the fluctuations and the gains. FIG. 3 is illustrative of anenergy band gap profile of a multiple quantum well structure provided ina conventional gallium nitride based semiconductor laser device oversapphire substrate as the first prior art. A GaN buffer layer isprovided on the sapphire substrate. An AlGaN cladding layer is providedover the GaN buffer layer. An InGaN quintuple quantum well active layeris provided over the AlGaN cladding layer.

[0210] The second and third prior arts relate to the gallium nitridebased semiconductor laser devices provided over the silicon carbidesubstrates. The second prior art semiconductor laser device has aphoto-luminescence wavelength distribution of about 150 meV of theactive layer in the cavity. The third prior art semiconductor laserdevice has a reduced photo-luminescence wavelength distribution of about90 meV of the active layer in the cavity. The reason for selectingsilicon carbide to the substrate material is mentioned in the aboveJapanese publication as follows.

[0211] In a short wavelength semiconductor laser device, sapphire havinga large lattice mismatch of 13% to the nitride based compoundsemiconductor is selected for the growth substrate, for which reason thedensity of dislocation in the active layer in the cavity is about 1×10¹⁰cm⁻². Notwithstanding, in the nitride based compound semiconductor, theprior art considered that the dislocation does not form non-luminescencecenter and does not provide any influence to the device performance. Theprior arts do not consider the density of the dislocations in the activelayer. Actually, however, the dislocation density has aninter-relationship with the compositional non-uniformity. As thedislocation density is decreased, then the compositional non-uniformityis also decreased. The use of the silicon carbide substrate largelyreduces the lattice miss-match to about 3%. The large reduction in thelattice miss-match results in a reduction in the dislocation densityinto not more than 1×10⁹ cm⁻² and at least to about 1×10⁷ cm⁻². Theshort wavelength semiconductor laser device with the suppressed multiplewavelength emission is realized. The descriptions of this paragraph areof the second and third prior arts.

[0212]FIG. 14 is a diagram illustrative of relationships between the“macroscopic fluctuation” and “microscopic fluctuation” in the indiumcompositional profile for the first type semiconductor laser device forlow output performance in accordance with the present invention, and thefirst to third prior arts. The horizontal axis represents the“microscopic fluctuation” in the indium compositional profile in thesub-micron order scale. The vertical axis represents the “macroscopicfluctuation” in the indium compositional profile in the order of notless than 1 micrometer. A hatched region represents the first typesemiconductor laser device for low output performance in accordance withthe present invention. The first to third prior arts have larger“microscopic fluctuation” not less than 100 meV. The first prior artprovides a differential gain of 5.8×10⁻¹⁷ cm², which is converted toabout 100 meV.

[0213] By contrast, in the first type semiconductor laser device for lowoutput performance in accordance with the present invention, the“microscopic fluctuation” is not more than 40 meV. The first typesemiconductor laser device for low output performance in accordance withthe present invention is different from the first to third prior arts inthat the “microscopic fluctuation” is reduced to not more than 40 meVand preferably not more than 20 meV.

[0214]FIG. 15 is a diagram illustrative of relationships between the“threshold mode gain” for one quantum well and the “microscopicfluctuation” in the indium compositional profile for the first typesemiconductor laser device for low output performance in accordance withthe present invention, and the first and third prior arts. Thehorizontal axis represents the “microscopic fluctuation” in the indiumcompositional profile in the sub-micron order scale. The vertical axisrepresents the “threshold mode gain” for one quantum well. A hatchedregion represents the first type semiconductor laser device for lowoutput performance in accordance with the present invention.

[0215] The first and third prior arts have higher threshold mode gainsthan 14 cm⁻¹. The conventional gallium nitride based semiconductor laserdevices of the prior arts generally have higher internal losses thanabout 40 cm⁻¹. If the number of the quantum wells is three or less, thenthe threshold mode gain for one quantum well is not less than 14 cm⁻¹ inconsideration of the mirror losses. The first type semiconductor laserdevice for low output performance in accordance with the presentinvention is different from the first and third prior arts in that thethreshold mode gain for one quantum well is reduced to not more than 12cm⁻¹ and preferably not more than 8 cm⁻¹ with effective reduction of theinternal loss.

[0216]FIG. 16 is a diagram illustrative of relationships between the“macroscopic fluctuation” and “microscopic fluctuation” in the indiumcompositional profile for the second type semiconductor laser device forhigh output performance in accordance with the present invention, andthe first to third prior arts. The horizontal axis represents the“microscopic fluctuation” in the indium compositional profile in thesub-micron order scale. The vertical axis represents the “macroscopicfluctuation” in the indium compositional profile in the order of notless than 1 micrometer. the present invention, and the first and thirdprior arts. The horizontal axis represents the “microscopic fluctuation”in the indium compositional profile in the sub-micron order scale. Thevertical axis represents the “threshold mode gain” for one quantum well.A hatched region represents the first type semiconductor laser device,for low output performance in accordance with the present invention.

[0217] The first and third prior arts have higher threshold mode gainsthan 14 cm⁻¹. The conventional gallium nitride based semiconductor laserdevices of the prior arts generally have higher internal losses thanabout 40 cm⁻¹. If the number of the quantum wells is three or less, thenthe threshold mode gain for one quantum well is not less than 14 cm⁻¹ inconsideration of the mirror losses. The first type semiconductor laserdevice for low output performance in accordance with the presentinvention is different from the first and third prior arts in that thethreshold mode gain for one quantum well is reduced to not more than 12cm⁻¹ and preferably not more than 8 cm⁻¹ with effective reduction of theinternal loss.

[0218]FIG. 16 is a diagram illustrative of relationships between the“macroscopic fluctuation” and “microscopic fluctuation” in the indiumcompositional profile for the second type semiconductor laser device forhigh output performance in accordance with the present invention, andthe first to third prior arts. The horizontal axis represents the“microscopic fluctuation” in the indium compositional profile in thesub-micron order scale. The vertical axis represents the “macroscopicfluctuation” in the indium compositional profile in the order of notless than 1 micrometer.

[0219] A hatched region represents the second type semiconductor laserdevice for high output performance in accordance with the presentinvention. The first to third prior arts have larger “microscopicfluctuation” not less than 100 meV. The first prior art provides adifferential gain of 5.8×10⁻¹⁷ cm², which is converted to about 100 meV.By contrast, in the second type semiconductor laser device for highoutput performance in accordance with the present invention, both the“microscopic fluctuation” and the “macroscopic fluctuation” are not morethan 40 meV. The second type semiconductor laser device for high outputperformance in accordance with the present invention is different fromthe first to third prior arts in that both the “microscopic fluctuation”and the “macroscopic fluctuation” are not more than 40 meV andpreferably not more than 20 meV.

[0220]FIG. 17 is a diagram illustrative of relationships between the“threshold mode gain” for one quantum well and the “microscopicfluctuation” in the indium compositional profile for the second typesemiconductor laser device for high output performance in accordancewith the present invention, and the first and third prior arts. Thehorizontal axis represents the “microscopic fluctuation” in the indiumcompositional profile in the sub-micron order scale. The vertical axisrepresents the “threshold mode gain” for one quantum weld.

[0221] A hatched region represents the second type semiconductor laserdevice for high output performance in accordance with the presentinvention. The first to third prior arts have larger “microscopicfluctuation” not less than 100 meV By contrast, in the second typesemiconductor laser device for high output performance in accordancewith the present invention, the “microscopic fluctuation” is not morethan 40 meV. The second type semiconductor laser device for high outputperformance in accordance with the present invention is different fromthe first and third prior arts in that the “microscopic fluctuation” isnot more than 40 meV and preferably not more than 20 meV.

[0222] For the present invention, it is important to reduce the“micro-fluctuations” in the indium composition profile and the band gapenergy profile of the luminescent layer. The micro-photo-luminescentmeasurement is applicable to only the measurement to the “macroscopicfluctuations” but inapplicable to the measurement to the “microscopicfluctuations”. In accordance with the present invention, the“microscopic fluctuation” is measured from the dependency on thephoto-luminescence life-time.

[0223] The following measurement method was carried out to measure the“microscopic fluctuation” in the band gap energy profile due to the“microscopic fluctuation” in the indium composition of the InGaN quantumwell layer as the luminescent layer provided in the InGaN quantum welllaser device. FIG. 11 is a diagram illustrative of variation in measuredphoto-luminescent life-time over temperature of the semiconductor laserdevice of FIG. 2. The photo-luminescent life-time was measured asfollows.

[0224] A light is irradiated onto a surface of the semiconductor laserdevice to cause an excitation of the laser, wherein the light comprisesa secondary higher harmonic wave of a pico-second titanium sapphirelaser, where the secondary higher harmonic wave has a wavelength of 370nanometers, and an output of 5 mW and a cyclic frequency of 80 MHz. Anemitted light from the semiconductor laser device is transmitted throughlenses to a spectroscope, wherein a spectral light is then detected by aphoto-multiplier, and a time resolution measurement is made by a singlephoton counting method. The time resolution measurement may also be madeby use of a streak camera. The temperature varies in the range of 5 K to300 K by a temperature-variable cryostat using a liquid helium.

[0225] The variation of the photo-luminescence over temperature has aninterrelationship with the standard deviation of the “microscopicfluctuation” of the band gap energy. Electrons excited by photons arccaptured by valley portions of the “microscopic fluctuation” of thepotential energy or the band gap energy, wherein the “microscopicfluctuation” of the potential energy or the band gap energy is providedby the “microscopic fluctuation” of the indium composition profile. Thecaptured electrons in the valley portions are inhibited to freely movefrom the valley portions over the potential barriers. This means thatthe probability of capturing the electrons into the defects ornon-radiation centers is low, whereby the photo-luminescence life-timeis long. If the temperature is increased, the captured electrons in thevalley portions receive heat energy and thermally excited, and thethermally excited electors may be movable over the potential barriers ofthe “microscopic fluctuation” of the potential energy or the band gapenergy. This means that the probability of capturing the electrons intothe defects or non-radiation centers is high, whereby thephoto-luminescence life-time is short.

[0226]FIG. 11 shows that if the temperature is increased from 100 K,then the photo-luminescence life-time is made short rapidly. The curveof FIG. 11 is fitted with and represented by the following equation.

τ_(PL) ⁻¹=τ₀ ⁻¹ +AT ^(½) exp(−T ₀ /T)  (1)

[0227] where τ_(PL) is the photo-luminescence life-time, T is thetemperature, τ₀, A, and T₀ are fitting parameters. If the temperature islow, then the electrons remain captured in the valley portions of thepotential having the “microscopic fluctuations”, for which reasonrecombination appears depending on the intrinsic life-time τ₀. At a lowtemperature, the second term of the above equation is ineffective andonly the first term is effective. This means that the life-time isconstant at τ₀. As the temperature is increased, the thermal excitationof electrons is caused. Assuming that the potential barrier provided bythe “microscopic fluctuation” is kT₀, where k is the Boltzmann'sconstant, a ratio of the excited carriers is proportional to exp(−T₀/T).Tie thermally excited carriers are movable over the potential barriersfrom the potential valleys provided by the “microscopic fluctuations”are then captured.

[0228] It is possible that the thermally excited carriers are capturedin the defects or the non-radiation center. The probability of capturingthe electrons is given by Nvs, where “N” is the density of the defects,“v” is the thermal velocity and “s” is the capture cross sectioned area.If the attention is drawn only onto the temperature dependency, then thethermal velocity is proportional to a square root of the temperature.Namely, Nvs=AT^(½) is established. If the temperature is increased, thenon-radiation recombination frequently appears based on the abovemechanism. The recombination velocity of the carriers depends onAT^(½)exp(−T₀/T). Namely, the recombination velocity of the carriers isgiven by the second term of the above equation. The parameter T0 isobtainable by the above fitting process. This parameter T0 is an indexparameter for the degree of the “microscopic fluctuation” of the indiumcomponent profile. For example, T0 is 460 K which is obtained from thepitting process based on FIG. 11.

[0229] The following descriptions will focus on the relationship betweenthe parameter T0 and the “microscopic fluctuation” of the band gapenergy profile. “kT0” corresponds to a thermal energy necessary forallowing electrons to freely move over the potential barriers providedby the “microscopic fluctuation” of the band gap energy profile. The“kT0” is proportional to the “microscopic fluctuation” of the potentialof the electrons distributed in the specific space.

[0230] If the “microscopic fluctuation” is processed by the potential ofthe electrons distributed in the two-dimensional space such as thequantum well, electrons having energies which are lower than aspatial-averaged potential value are localized and are not free to moveover the potential barriers, whilst electrons having energies which arelower than the spatial-averaged potential value are free to move overthe potential barriers. Those are deduced from the classical percolationtheory. Thus, the “kT0” may be considered to be a difference in energylevel from the bottom of the valley portions to the averaged potentiallevel.

[0231] Assuming that the spatial distribution of the potential energy isthe normal distribution with a standard deviation σ_(e), then the valleyof the potential is lower in energy level by about 2 σ_(e) than theaveraged potential value, whereby σ_(e)=0.5 kT0 is derived. The standarddeviation σ_(g) of the “microscopic fluctuation” of the band gap energyof InGaN corresponds to a sum of the “microscopic fluctuation” inpotential of the conduction band and the “microscopic fluctuation” inpotential of the valence band. In Applied Physics Letters vol. 68, p.2541, 1996, Martin et al. address that if a band off-set ratio of theconduction band and the valence band of the InGaN based compoundsemiconductor is 3:7, then σ_(g)=3.33 σ_(e)=1.67 kT0. The standarddeviation σ_(g) of the “microscopic fluctuation” of the band gap energyof InGaN is found from T0 by use of the above equation. In case of FIG,11, the standard deviation σ_(g) of the “microscopic fluctuation” of theband gap energy is found to be a large value, for example, 66 meV.

[0232] The micro-photo-luminescent measurement with a micro-beam spot ofa diameter of 1 micrometers to the semiconductor laser device shown inFIG. 2 was carried out. The distribution of the photo-luminescent peakwavelength is within the range of −1 nanometer to +1 nanometer, whichcorresponds to a range of −9 meV to +9 meV. The fluctuation of theindium composition profile in the scale over 1 micrometer could not bemeasured. Notwithstanding, the fluctuation the indium compositionprofile was measured by a different measurement method based on atemperature-dependency of the photo-luminescence life-time. This meansthat the fluctuation of the indium composition profile is the“microscopic fluctuation” of the sub-micron order scale which is notmeasurable by the photo-luminescence measurement.

[0233] In order to reduce the “macroscopic fluctuations” in the indiumcomposition profile and the band gap profile of the active layer, it iseffective to control the partial pressure of an ammonium gas, forexample, not more than 110 hPa in the metal organic vapor phase epitaxyfor forming at least the luminescent layer for the purpose of adjustingthe growth rate. The control to the partial pressure of the ammonium gassuppresses the “macroscopic fluctuation” of the energy band gap within20 meV. For controlling the “microscopic fluctuation” of the energy bandgap within 75 meV to 200 meV in addition to the reduction of the“macroscopic fluctuations”, it is effective to carry out a heattreatment at a relatively high temperature after the multilayerstructure has been grown under the above control to the partial pressureof the ammonium gas.

[0234] A temperature of the heat treatment may be not less than 850° C.,and preferably not less than 900° C., but not more than 1200° C. Thenecessary time for the heat treatment may generally be not less than 40minutes. This heat treatment is carried out in order to form the“microscopic fluctuation” of the indium compositional profile. A lowtemperature gentle heat treatment, which may usually be used for formingan electrode, is not usable.

[0235] In accordance with the present invention, in order to reduce theinternal loss, it is effective that a self confinement hetero-structurelayer in a p-type electrode side comprises a non-doped layer, and that agrowth temperature is kept high, for example, not less than 1100° C. Ingeneral, the self confinement hetero-structure layer in the p-typeelectrode side is doped with magnesium, resulting in crystalimperfection and formation of impurity level. These crystal imperfectionand impurity level formation reduce the internal loss. In accordancewith the present invention, in order to reduce the internal loss, theself confinement hetero-structure layer in the p-type electrode side isnot doped and further the growth conditions arc properly selected.

[0236] In accordance with the present invention, the photo-luminescencepeak wavelength distribution is preferably not more than 40 meV and morepreferably not more than 20 meV for the purpose of effectively reducingthe threshold current. If the photo-luminescence peak wavelengthdistribution is ranged to be much higher value than 40 meV, then thethreshold current is also high and the power consumption is also high.

[0237] In accordance with the present invention, the standard deviationof the “microscopic fluctuation” of the energy band gap of theluminescent layer is preferably in the range of 75 meV to 200 meV, andmore preferably in the range of 80 meV to 150 meV, and further thostandard deviation of the “microscopic fluctuation” of the indiumcompositional profile of the luminescent layer is preferably in therange of 0.125 to 0.333, and more preferably in the range of 0.133 to0.266 for effectively reducing the threshold current of the laserdevice.

[0238] The base layer means a layer over which layers constituting thelaser diode are provided. As described above, the base layer maycomprise a crystal growth substrate of the gallium nitride basedmaterial such as GaN and AlGaN. Alternatively, the base layer maycomprise a base layer provided over any substrate, for example, thesemiconductor or semi-insulating substrate. For example, thesemi-insulating substrate may comprise a sapphire substrate. The word“surface dislocation density” means a density of through dislocation onthe surface of the layer. The base layer having the surface dislocationdensity of less than 1×10⁸ cm⁻² may, for example, be obtained by eithera facet-initiated epitaxial lateral over growth method or apendio-epitaxy method.

[0239] The formation of the base layer in the facet-initiated epitaxiallateral over growth method may be made as follows. A thin GaN layer isformed over a sapphire substrate. Stripe-shaped SiO2 masks are formed onthe thin GaN layer. A selective lateral growth of the GaN layer from anopening portion of the stripe-shaped SiO2 masks is carried out, so thatthe GaN layer has a reduced surface dislocation density, whereinextensions of dislocations are blocked by the SiO2 masks and alsochanged in direction toward a lateral direction parallel to the surfaceof the substrate in the selective lateral growth. This facet-initiatedepitaxial lateral over growth method is disclosed in 1999 AppliedPhysics vol. 68, 7, pp. 774-779.

[0240] The formation of the base layer in the pendio-epitaxy method maybe made as follows. A low temperature buffer layer is formed over asubstrate. A single crystal GaN layer is formed over the buffer layer.Etching masks are provided on the single crystal GaN layer. A selectiveetching to the single crystal GaN layer is carried out by use of theetching masks to form a stripe-shaped single crystal GaN pattern. Acrystal growth from either a top surface or a side face of thestripe-shaped single crystal GaN pattern is made, thereby forming a baselayer having a reduced surface dislocation density. This pendio-epitaxymethod was reported by Tsvetankas. Zheleva et al. in MRS Internet J.Nitride Semiconductor Res. 4S1, G3 38 (1999).

[0241] The following method is also available to obtain the substratehaving a further reduced dislocation density. A buffer layer is formedon the sapphire substrate. A gallium nitride based single crystal layeris formed on the buffer layer. The gallium nitride based single crystallayer is selectively etched to form gallium nitride based single crystalislands over the buffer layer. The gallium nitride based single crystalislands are used as seeds for crystal growth to form the base layerhaving the reduced surface dislocation density. In place of theselective etching process, growth conditions for the gallium, nitridebased single crystal layer may be selected to grow gallium nitride basedsingle crystal islands over the buffer layer.

[0242] In accordance with the present invention, the surface dislocationdensity of the base layer is preferably less than 1×10⁸ cm⁻², and morepreferably 1×10⁷ cm⁻². If the dislocation density of the base layer ismuch higher than 1×10⁸ cm⁻², then it is difficult to realize the longlife-time of the device even the “microscopic fluctuations” in theindium composition profile and the band gap energy profile are reducedand the differential gain is increased. If the dislocation density ofthe base layer is suppressed less than 1×10⁸ cm⁻², particularly lessthan 1×10⁷ cm⁻², a multiplier effect of the low dislocation density andthe reduced “microscopic fluctuations” is obtained. This allowsimprovement in the life-time of the device with keeping the good deviceperformances. The surface dislocation density is measurable by the knownmethods, for example, by measuring etch-pits of the layer or observationto a sectioned area of the layer by a transmission electron microscope.The base layer having the reduced dislocation density is obtainable byusing the single crystal islands as seeds for the crystal growth. Thissubstrate with the reduced dislocation density can be obtained by asingle crystal growth from single crystal islands.

[0243] The base layer may comprise a low dislocation single crystal GaNlayer grown over the substrate by the facet-initiated epitaxial lateralover growth. The base layer may also comprise a low dislocation singlecrystal AlGaN layer grown over the substrate by the facet-initiatedepitaxial lateral over growth. The base layer may also comprise a lowdislocation single crystal GaN layer grown over the substrate by thependio-epitaxy method. The base layer may also comprise a lowdislocation single crystal AlGaN layer grown over the substrate by thependio-epitaxy method. The base layer may also comprise a lowdislocation single crystal GaN layer grown by the crystal growth fromthe single crystal gallium nitride islands over the substrate. The baselayer may also comprise a low dislocation single crystal GaN layer grownby the crystal growth from the single crystal aluminum gallium nitrideislands over the substrate. The substrate may optionally be removedafter the low dislocation single crystal GaN or AlGaN layer has beengrown on the substrate. Since the base layer is of the low surfacedislocation density, the base layer is not inclusive of a lowtemperature buffer layer deposited at a low temperature.

[0244] As described above, the base layer comprises one of the galliumnitride based materials such as AlGaN and GaN. The word “gallium nitridebased material” means that any materials which include at least bothnitrogen and gallium. The selection of any one of AlGaN and GaN for thebase layer is preferable for improving both an optical confinement rateand the device life-time. In case of a gallium nitride basedsemiconductor laser diode, the cladding layer may be made of AlGaN,wherein it is preferable for obtaining a desired high opticalconfinement rate that a compositional ratio of aluminum in the claddinglayer is high and also that a thickness of the cladding layer is thick.

[0245] If the semiconductor laser diode is applied to emit a laser beamhaving a luminescent wavelength in the range of 390-430 nanometers forthe purpose of optical disk, it is preferable that the thickness of thecladding layer is 1 micrometer or more and the aluminum compositionalratio is not less than 0.05 and more preferably not less than 0.07. Inthis case, selection of GaN or AlGaN for the base layer is preferable,so as to make both thermal expansion coefficient and lattice constantsimilar between the base layer and the cladding layer, whereby aresidual strain of the cladding layer is reduced as compared to when thebase layer is different in material from the cladding layer.

[0246] The reduction in residual strain of the cladding layer iseffective for preventing the deterioration of the active layer in thehigh temperature operation. The above selection of the material for thebase layer also increases the available range of the thickness and thealuminum composition rate of the cladding layer, and also makes it easyto obtain a high optical confinement rate.

[0247] In order to realize the reductions in the “microscopicfluctuations” in the indium composition profile and the band gap energyprofile of the luminescent layer and also to obtain the desired highdifferential gain, it is preferable to consider the growth conditions ofthe luminescent layer. As the ammonium gas partial pressure isdecreased, then the obtainable differential gain is increased. In orderto obtain the desirable high differential gain and also reduce the above“micro-fluctuations” in the indium composition profile and the band gapenergy profile, it is preferable that the ammonium gas partial pressureis not less than the predetermined level, for example, 110 hPa and morepreferably 95 hPa.

[0248] The threshold current depends on the number of the quantum wells,for which reasons it is preferable for the first type semiconductorlaser device showing the low output performance that the number of thequantum wells is not more than three in view of reducing a thresholdcurrent for the purpose of possible reduction of the power consumption.This limitation in the number of the quantum wells allows a uniformcarrier injection into the quantum wells. If the number of the quantumwells is large, for example, not less than 4, then it is likely todifficult to obtain the uniform hole injection into the quantum wells.

[0249] One or some of the quantum wells are insufficient in carrierdensity, whereby the internal losses are low In Applied Physics vol. 73,1998, pp. 2775-2777, Domen et al. reported that the carrier injectionsto the three quantum wells are uniform, but the carrier injections tothe five quantum wells are not uniform.

[0250] The following descriptions will focus on the method of measuringthe reflectance of the semiconductor laser diode. The reflectance “R” ofthe sample laser is given by R=(n−1/n+1)², where “n” is the refractiveindex of the semiconductor, provided that the semiconductor is simplycleaved without coating. It was known that the refractive index of GaNis about 2.553 if the wavelength of the laser beam is 400 nanometers. Inthis case, the reflectance “R” is 19%.

[0251] A dielectric multilayer structure may be usable for obtaining ahighly reflective mirror, wherein the dielectric multilayer structurecomprises alternating laminations of a high refractive index dielectricfilm and a low refractive index dielectric film. The reflectance “R”depends on the individual refractive indexes of the used materials,individual thickness of the films and the number of the laminated films.TiO₂ has a refractive index of 2.31. SiO₂ has a refractive index of1.44.

[0252]FIG. 13 is a diagram illustrative of reflective spectrums whichrepresent variations in reflectance “R” over wavelength, wherein SiO₂films and TiO₂ films are alternately laminated by one pair, two pairs,three pairs and four pairs, where the SiO₂ films and TiO₂ films have athickness of 100 nanometers. The reflectance “R” comes large at awavelength of about 400 nanometers. The reflectance “R” at a wavelengthof about 400 nanometers depends on the number of pairs, namely on thenumber of the laminations. In case of the single pair of the SiO₂ filmand TiO₂ film, the maximum value of the reflectance “R” is approximately50%. In case of the two pair of the SiO₂ film and TiO₂ film, the maximumvalue of the reflectance “R” is approximately 80%.

[0253] In case of the three pair of the SiO₂ film and TiO₂ film, themaximum value of the reflectance “R” is approximately 90%. In case ofthe four pair of the SiO₂ film and TiO₂ film, the maximum value of thereflectance “R” is over 90%. The reflectance is calculated from thematerials, thicknesses and the number of laminations.

[0254] There is another method of measuring the reflectance of thehighly reflective coating, wherein the semiconductor laser diode isused. First and second outputs P1 and P2 from first and secondreflectances R1 and R2 of the first and second facets of thesemiconductor laser diode have a relationship given byP1/P2=(1−R1)/(1−R2)×(R2/R1)^(0.5). One of the first and secondreflectances R1 and R2 is calculated from a ratio of P1/P2 and anotherof the first and second reflectances R1 and R2. If one of the first andsecond facets is uncoated, then the estimated reflectance of theuncoated facet is 19%. This method is effective to calculate theremaining reflectance of the coated facet.

[0255] The mirror loss can be obtained from the laser oscillationconditions and the above first and second reflectances R1 and R2. Themirror loss “α_(m)” is given by α_(m)=½L×1n(1/R1/R2), where “L” is thecavity length. The mirror loss can be obtained from the reflectances anthe length of the cavity.

[0256] Usually, the dielectric multilayer mirror such as alternatinglaminations of SiO₂ film and TiO₂ film is used for the highly reflectivecoat of the nitride based semiconductor laser diode, and the reflectancefactor is not less than 80%. If the first and second facets areHR-coated, then a mirror loss is approximated to be 1 cm⁻¹. If one ofthe first and second facets is HR-coated and a cavity length is about400 micrometers, then a mirror loss is approximated to be 20 cm⁻¹.

[0257] The internal loss “α_(i)” can be investigated based on thecurrent-output characteristics. If the semiconductor laser device havingthe first and second reflectances R1 and R2, an optical output “P1” fromthe first facet having the first reflectance R1 is given by:

P1={α_(m)/(α_(i)+α_(m))}×[{(1−R1){square root}(R2)}/{(1−{squareroot}(R1R2))×({square root}(R1)+{square root}(R2))}]×Vd×(I−Ith)

[0258] where “I” is the current, “Ith” is the threshold current, “Vd” isthe junction potential, “α_(m)” is the mirror loss and “α_(i)” is theinternal loss. The junction potential “Vd” may be approximated to bealmost equal to an optical energy corresponding to the oscillationwavelength. Therefore, the internal loss can be estimated byinvestigating the current-output characteristic if the reflectances andthe mirror loss have been know.

[0259] The threshold mode gain can be obtained from the sum of theinternal loss and the mirror loss, in view that the laser oscillationcan be obtained when the gain and the loss are balanced to each other.

FIRST EXAMPLE

[0260] A first example according to the present invention will bedescribed in detail with reference to the drawings. An n-GaN substratewith a low dislocation density was prepared by the above describedfacet-initiated epitaxial lateral over growth. The prepared substratewas made into contact with a phosphoric acid based solution to formetching-pits. The substrate was then measured in density of theetching-pits for measuring a surface dislocation density. It wasconfirmed that the measured surface dislocation density was 5.0×10⁷cm⁻².

[0261] This n-GaN substrate with the low surface dislocation density wasused for forming a gallium nitride based laser diode. FIG. 12A is across sectional elevation view illustrative of a semiconductor laserdiode in a first example in accordance with the present invention. Ann-type cladding layer 22 was formed on a top surface of the n-GaNsubstrate 21, wherein the n-type cladding layer 22 comprises an Si-dopedn-type Al_(0.1)Ga_(0.9)N layer having a silicon impurity concentrationof 4×10¹⁷ cm⁻³ and a thickness of 1.2 micrometers. An n-type opticalconfinement layer 23 was formed on a top surface of the n-type claddinglayer 22, wherein the n-type optical confinement layer 23 comprises anSi-doped n-type GaN layer having a silicon impurity concentration of4×10¹⁷ cm⁻³ and a thickness of 0.1 micrometer.

[0262] A multiple quantum well active layer 24 was formed on a topsurface of the n-type optical confinement layer 23, wherein the multiplequantum well active layer 24 comprises three In_(0.2)Ga_(0.8)N welllayers having a thickness of 4 nanometers and Si-dopedIn_(0.05)Ga_(0.95)N potential barrier layers having a silicon impurityconcentration of 5×10¹⁸ cm⁻³ and a thickness of 5 micrometers. A caplayer 25 was formed on a top surface of the multiple quantum well activelayer 24, wherein the cap layer 25 comprises an Mg-doped p-typeAl_(0.2)Ga_(0.8)N layer. An undoped optical confinement layer 26 wasformed on a top surface of the cap layer 25, wherein the undoped opticalconfinement layer 26 comprises an undoped GaN layer having a thicknessof 0.1 micrometer. A p-type cladding layer 27 was formed on a topsurface of the undoped optical confinement layer 26, wherein the p-typecladding layer 27 comprises an Mg-doped p-type Al_(0.1)Ga_(0.9)N layerhaving a magnesium impurity concentration of 2×10¹⁷ cm⁻³ and a thicknessof 0.5 micrometers.

[0263] A p-type contact layer 28 was formed on a top surface of thep-type cladding layer 27, wherein the p-type contact layer 28 comprisesan Mg-doped p-type GaN layer having a magnesium impurity concentrationof 2×10¹⁷ cm⁻³ and a thickness of 0.1 micrometer.

[0264] Those layers 22, 23, 24, 25, 26, 27, and 28 were formed by a lowpressure metal organic vapor phase epitaxy method under a pressure of200 hPa. A partial pressure of the ammonium gas for nitrogen source wasmaintained at 53 hPa. TMG was used for the Ga source material. TMA wasused for the Al source material. TMI was used for the In sourcematerial. The growth temperature was maintained at 1050° C. except whenthe InGaN multiple quantum well active layer 24 and the undoped opticalconfinement layer 26 were grown. In the growth of the InGaN multiplequantum well active layer 24, the growth temperature was maintained at780° C. In the growth of the undoped optical confinement layer 26, thegrowth temperature was maintained at 1150° C.

[0265] After the formed structure was subjected to a heat treatment at900° C. for 1 hour, a dry etching process was then carried out toselectively etch the p-type cladding layer 27 and the p-type contactlayer 28 thereby forming a mesa structure 29. A silicon dioxide film 30was formed on the mesa structure 29 and the upper surfaces of the p-typecontact layer 28. The silicon dioxide film 30 was selectively removedfrom the top surface of the mesa structure 29 by use of an exposuretechnique, whereby the top surface of the p-type contact layer 28 wasshown and a ridged structure was formed. An n-type electrode 31 wasformed on a bottom surface of the substrate 21, wherein the n-typeelectrode 31 comprises laminations of a titanium layer and an aluminumlayer.

[0266] A p-type electrode 32 was formed on a top surface of the p-typecontact layer 28, wherein the p-type electrode 32 comprises laminationsof a nickel layer and a gold layer. The above structure was then cleavedto form first and second facets which defines a cavity length of 300micrometers. Both the first and second facets were then coated with ahighly reflective coat of a reflectance factor of 80%, wherein thehighly reflective coat comprises laminations of titanium dioxide filmand silicon dioxide film.

[0267] For the method of forming the above laser device, the followingthree points are important. First, the multi-layered structure was grownunder the condition of the low partial pressure of ammonium. Second, aheat treatment was then carried out at about 900° C. for one hour afterthe multi-layered structure had been grown. Third, the GaN opticalconfinement layer 26 was undoped and its growth temperature was high,for example, 1150° C.

[0268] The first important point is to reduce both the “microscopicfluctuation” and the “macroscopic fluctuation” in the composition of thequantum wells in the active layer. The present inventors discovered thatafter the quantum wells having the small “microscopic fluctuation” andthe small “macroscopic fluctuation” has been grown, then the hightemperature heat treatment is carried out thereby to cause that only the“microscopic fluctuation” becomes large whilst the “macroscopicfluctuation” remains as small. The present inventors also discoveredthat an optical absorption into the GaN optical confinement layer is themain cause for the internal loss. In order to reduce the opticalabsorption into the GaN optical confinement layer, it is effective toimprove the crystal quality. To improve the crystal quality, it iseffective to increase the growth temperature of the GaN opticalconfinement layer. In addition, in order to reduce the opticalabsorption through the impurity level, Mg is not doped into the GaNoptical confinement layer.

[0269] It was confirmed that the semiconductor laser device exhibits thefollowing characteristics. The usage of the semiconductor laser deviceis the low output laser diode. The number of the quantum wells is 3. Thecavity length was 300 micrometers. The threshold mode gain for thesingle quantum well is 6.5 cm⁻¹. The first mirror reflectance of thefirst facet with HR-coat, from which the light is emitted, is 80%. Thesecond mirror reflectance of the second facet with HR-coat opposite tothe first facet is also 80%. The mirror loss is 7.4 cm⁻¹. The internalloss is 12 cm⁻¹. The slope efficiency is 0.57 (W/A). The standarddeviation of the microscopic fluctuation of the indium composition is0.167. The standard deviation of the microscopic fluctuation of the bandgap energy is 100 meV. The differential gain “dg/dN” is 0.6×10⁻²⁰ m².The threshold current density is 0.8 (kA/cm²). The photo-luminescencepeak wavelength distribution is within 19 meV. The threshold current issufficiently low.

[0270] The “macroscopic fluctuation” in the indium composition wasmeasured by the microscopic photo-luminescence measurement with theresolving power of 1 micrometer. It was confirmed that thephoto-luminescent wavelength distribution was not more than 20 meV.

[0271] Further, the “microscopic fluctuation” in the indium compositionwas measured by the relaxation frequency measurement which measures thedifferential gain. It was confirmed that the “microscopic fluctuation”was 100 meV.

[0272] Furthermore, the “microscopic fluctuation” in the indiumcomposition was measured by observation of cathode luminescence. In thecathode luminescence observation, after the cap layer was formed overthe multiple quantum well active layer, the growth process wasdiscontinued to form evaluation-purpose samples. Electron beams areirradiated onto the evaluation-purpose samples with concurrentspectroscope for conducting mapping process at a predeterminedwavelength, at an acceleration voltage of 3 kV and at room temperature.The cathode luminescence was observed in the range of 400-500nanometers. FIG. 18 is a photograph of the cathode luminescence image inexample 1 of the present invention As a result, it was confirmed thatthe samples of the example 1 of the present invention are free of the,“macroscopic fluctuation” but have the “microscopic fluctuation”.

SECOND EXAMPLE

[0273] A second example according to the present invention will bedescribed in detail with reference to the drawings. An n-GaN substratewith a low dislocation density was prepared by the above describedfacet-initiated epitaxial lateral over growth. The prepared substratewas made into contact with a phosphoric acid based solution to formetching-pits. The substrate was then measured in density of theetching-pits for measuring a surface dislocation density. It wasconfirmed that the measured surface dislocation density was 5.0×10⁷cm⁻². The laser device of this second example is different from thefirst example in the high output performance and the single quantum wellactive layer.

[0274] This n-GaN substrate with the low surface dislocation density wasused for forming a gallium nitride based laser diode. FIG. 12B is across sectional elevation view illustrative of a semiconductor laserdiode in a second example in accordance with the present invention. Ann-type cladding layer 42 was formed on a top surface of the n-GaNsubstrate 41, wherein the n-type cladding layer 42 comprises an Si-dopedn-type Al_(0.1)Ga_(0.9)N layer having a silicon impurity concentrationof 4×10¹⁷ cm⁻³ and a thickness of 1.2 micrometers. An n-type opticalconfinement layer 43 was formed on a top surface of the n-type claddinglayer 42, wherein the n-type optical confinement layer 43 Comprises anSi-doped n-type GaN layer having a silicon impurity concentration of4×10¹⁷ cm⁻³ and a thickness of 0.1 micrometer.

[0275] A single quantum well active layer 44 was formed on a top surfaceof the n-type optical confinement layer 43, wherein the single quantumwell active layer 44 comprises a single In_(0.2)Ga_(0.8)N well layerhaving a thickness of 3 nanometers and Si-doped In_(0.05)Ga_(0.95)Npotential barrier layers having a silicon impurity concentration of5×10¹⁸ cm⁻³ and a thickness of 5 micrometers. A cap layer 45 was formedon a top surface of the multiple quantum well active layer 44, whereinthe cap layer 45 comprises an Mg-doped p-type Al_(0.2)Ga_(0.8)N layer.

[0276] An undoped optical confinement layer 46 was formed on a topsurface of the cap layer 45, wherein the undoped optical confinementlayer 46 comprises an undoped GaN layer having a thickness of 0.1micrometer. A p-type cladding layer 47 was formed on a top surface ofthe undoped optical confinement layer 46, wherein the p-type claddinglayer 47 comprises an Mg-doped p-type Al_(0.1)Ga_(0.9)N layer having amagnesium impurity concentration of 2×10¹⁷ cm⁻³ and a thickness of 0.5micrometers. A p-type contact layer 48 was formed on a top surface ofthe p-type cladding layer 47, wherein the p-type contact layer 48comprises an Mg-doped p-type GaN layer having a magnesium impurityconcentration of 2×10¹⁷ cm⁻³ and a thickness of 0.1 micrometer.

[0277] Those layers 42, 43, 44, 45, 46, 47, and 48 were formed by a lowpressure metal organic vapor phase epitaxy method under a pressure of200 hPa. A partial pressure of the ammonium gas for nitrogen source wasmaintained at 53 hPa. TMG was used for the Ga source material. TMA wasused for the Al source material. TMI was used for the In sourcematerial. The growth temperature was maintained at 1050° C. except whenthe InGaN single quantum well active layer 44 and the undoped opticalconfinement layer 46 were grown. In the growth of the InGaN singlwquantum well active layer 44, the growth temperature was maintained at780° C. In the growth of the undoped optical confinement layer 46, thegrowth temperature was maintained at 1150° C.

[0278] After the formed structure was subjected to a heat treatment at900° C. for 1 hour, a dry etching process was then carried out toselectively etch the p-type cladding layer 47 and the p-type contactlayer 48 thereby forming a mesa structure 49. A silicon dioxide film 50was formed on the mesa structure 49 and the upper surfaces of the p-typecontact layer 48. The silicon dioxide film 50 was selectively removedfrom the top surface of the mesa structure 49 by use of an exposuretechnique, whereby the top surface of the p-type contact layer 48 wasshown and a ridged structure was formed.

[0279] An n-type electrode 51 was formed on a bottom surface of thesubstrate 41, wherein the n-type electrode 51 comprises laminations of atitanium layer and an aluminum layer. A p-type electrode 52 was formedon a top surface of the p-type contact layer 48, wherein the p-typeelectrode 52 comprises laminations of a nickel layer and a gold layer.The above structure was then cleaved to form first and second facetswhich defines a cavity length of 300 micrometers. Only the second facetwas then coated with a highly reflective coat of a reflectance factor of95%, wherein the highly reflective coat comprises laminations oftitanium dioxide film and silicon dioxide film. The first facet wasuncoated.

[0280] For the method of forming the above laser device, the followingthree points are important. First, the multi-layered structure was grownunder the condition of the low partial pressure of ammonium. Second, aheat treatment was then carried out at about 900° C. for one hour afterthe multi-layered structure had been grown. Third, the GaN opticalconfinement layer 46 was undoped and its growth temperature was high,for example, 1150° C.

[0281] The first important point is to reduce both the “microscopicfluctuation” and the “macroscopic fluctuation” in the composition of thequantum well in the active layer. The present inventors discovered thatafter the quantum well having the small “microscopic fluctuation” andthe small “macroscopic fluctuation” has been grown, then the hightemperature heat treatment is carried out thereby to cause that only the“microscopic fluctuation” becomes large whilst the “macroscopicfluctuation” remains small. The present inventors also discovered thatan optical absorption into the GaN optical confinement layer is the maincause for the internal loss.

[0282] In order to reduce the optical absorption into the GaN opticalconfinement layer, it is effective to improve the crystal quality. Toimprove the crystal quality, it is effective to increase the growthtemperature of the GaN optical confinement layer. In addition, in orderto reduce the optical absorption through the impurity level, Mg is notdoped into the GaN optical confinement layer.

[0283] It was confirmed that the semiconductor laser device exhibits thefollowing characteristics. The usage of the semiconductor laser deviceis the high output laser diode. The number of the quantum well is 1. Thecavity length was 500 micrometers. The threshold mode gain for thesingle quantum well is 29 cm⁻¹. The first mirror reflectance of thefirst facet uncoated, from which the light is emitted, is 19%. Thesecond mirror reflectance of the second facet with HR-coat opposite tothe first facet is also 95%. The mirror loss is 17 cm⁻¹. The internalloss is 12 cm⁻¹. The slope efficiency is 1.7 (W/A). The standarddeviation of the microscopic fluctuation of the indium composition is0.0083. The standard deviation of the microscopic fluctuation of theband gap energy is 5 meV. The differential gain “dg/dN” is 2.2×10⁻²⁰ m².The threshold current density is 0.8 (kA/cm²). The photo-luminescencepeak wavelength distribution is within 17 meV. The threshold current issufficiently low.

[0284] Although the invention has been described above in connectionwith several preferred embodiments therefor, it will be appreciated thatthose embodiments have been provided solely for illustrating theinvention, and not in a limiting sense. Numerous modifications andsubstitutions of equivalent materials and techniques will be readilyapparent to those skilled in the art after reading the presentapplication, and all such modifications and substitutions are expresslyunderstood to fall within the true scope and spirit of the appendedclaims.

What is claimed is:
 1. A semiconductor device having a semiconductormulti-layer structure which includes at least an active layer having atleast a quantum well, and said active layer further including at least aluminescent layer of In_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein athreshold mode gain of each of said at least quantum well is not morethan 12 cm⁻¹, and wherein a standard deviation of a microscopicfluctuation in a band gap energy of said at least luminescent layer isin the range of 75 meV to 200 meV.
 2. The semiconductor device asclaimed in claim 1, wherein a differential gain “dg/dn” of said at leastactive, layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).
 3. Thesemiconductor device as claimed in claim 1, wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfies α₁≦12×n−α_(m)(cm⁻¹), where “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well.
 4. The semiconductor device as claimed in claim 1,wherein said semiconductor device has a slope efficiency “S” (W/A) whichsatisfies: S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{squareroot}(R ₁ R ₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” isa first reflectance of a first cavity facet, from which a light isemitted, “R₂” is a second reflectance of a second cavity facet oppositeto said first cavity facet, “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 5. The semiconductor device asclaimed in claim 4, wherein said semiconductor device has a cavitylength “L” of not less than 200 micrometers, and each of said first andsecond reflectances “R₁” and “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S≧1.4/n (W/A).
 6. Thesemiconductor device as claimed in claim 1, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 7. The semiconductor device as claimed in claim 1, whereinsaid semiconductor multi-layer structure comprises agallium-nitride-based multilayer structure.
 8. The semiconductor deviceas claimed in claim 7, wherein said gallium-nitride-based multi-layerstructure extends over a gallium-nitride-based substrate.
 9. Thesemiconductor device as claimed in claim 7, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 10. The semiconductor device as claimed in claim 7, whereinsaid gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².11. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of said at least quantum well is not more than 12 cm⁻¹, andwherein a differential gain “dg/dn” of said at least active layersatisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).
 12. The semiconductordevice as claimed in claim 11, wherein a standard deviation of amicroscopic fluctuation in a band gap energy of said at leastluminescent layer is in the range of 75 meV to 200 meV.
 13. Thesemiconductor device as claimed in claim 11, wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 14. The semiconductor device asclaimed in claim 11, wherein said semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R ₂)}/{(1−{square root}(R ₁ R ₂))×({square root}(R₁)+{square root}(R ₂))}], where “R₁” is a first reflectance of a firstcavity facet, from which a light is emitted, “R₂” is a secondreflectance of a second cavity facet opposite to said first cavityfacet, “α_(m)” is a mirror loss, and “n” is a number of said at leastquantum well.
 15. The semiconductor device as claimed in claim 14,wherein said semiconductor device has a cavity length “L” of not lessthan 200 micrometers, and each of said first and second reflectances“R₁” and “R₂” is not less than 80% and less than 100%, and said slopeefficiency “S” satisfies S≧1.4/n (W/A).
 16. The semiconductor device asclaimed in claim 11, wherein said semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.17. The semiconductor device as claimed in claim 11, wherein saidsemiconductor multi-layer structure comprises a gallium-nitride-basedmulti-layer structure.
 18. The semiconductor device as claimed in claim17, wherein said gallium-nitride-based multi-layer structure extendsover a gallium-nitride-based substrate.
 19. The semiconductor device asclaimed in claim 17, wherein said gallium-nitride-based multi-layerstructure extends over a sapphire substrate.
 20. The semiconductordevice as claimed in claim 17, wherein said gallium-nitride-basedmulti-layer structure extends over a substrate having a surfacedislocation density of loss than 1×10⁸/cm².
 21. A semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and said active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well, and wherein a standard deviationof a microscopic fluctuation in a band gap energy of said at leastluminescent layer is in the range of 75 meV to 200 meV.
 22. Thesemiconductor device as claimed in claim 21, wherein a differential gain“dg/dn” of said at least active layer satisfies 0.5×10⁻²⁰(m²)≦dg/dn≦0.7×10⁻²⁰ (m²).
 23. The semiconductor device as claimed inclaim 21, wherein a threshold mode gain of each of said at least quantumwell is not more than 12 cm⁻¹.
 24. The semiconductor device as claimedin claim 21, wherein said semiconductor device has a slope efficiency“S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R₂)}/{(1−{square root}(R ₁ R ₂))×({square root}(R ₁)+{square root}(R₂))}], where “R₁” is a first reflectance of a first cavity facet, fromwhich a light is emitted, “R₂” is a second reflectance of a secondcavity facet opposite to said first cavity facet, “α_(m)” is a mirrorloss, and “n” is a number of said at least quantum well.
 25. Thesemiconductor device as claimed in claim 24, wherein said semiconductordevice has a cavity length “L” of not less than 200 micrometers, andeach of said first and second reflectances “R₁” and “R₂” is not lessthan 80% and less than 100%, and said slope efficiency “S” satisfiesS≧1.4/n (W/A).
 26. The semiconductor device as claimed in claim 21,wherein said semiconductor device has a photo-luminescence peakwavelength distribution of not more than 40 meV.
 27. The semiconductordevice as claimed in claim 21, wherein said semiconductor multi-layerstructure comprises a gallium-nitride-based multi-layer structure. 28.The semiconductor device as claimed in claim 27, wherein saidgallium-nitride-based multi-layer structure extends over agallium-nitride-based substrate.
 29. The semiconductor device as claimedin claim 27, wherein said gallium-nitride-based multi-layer structureextends over a sapphire substrate.
 30. The semiconductor device asclaimed in claim 27, wherein said gallium-nitride-based multi-layerstructure extends over a substrate having a surface dislocation densityof less than 1×10⁸/cm².
 31. A semiconductor device having asemiconductor multi-layer structure which includes at least an activelayer having at least a quantum well, and said active layer furtherincluding at least a luminescent layer of In_(x)Al_(y)Ga_(1-x-y)N(0<x<1, 0≦y≦0.2), wherein said semiconductor device has an internal loss“α_(i)” (cm⁻¹) which satisfies α_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” isa mirror loss, and “n” is a number of said at least quantum well, andwherein a differential gain “dg/dn” of said at least active layersatisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).
 32. The semiconductordevice as claimed in claim 31, wherein a standard deviation of amicroscopic fluctuation in a band gap energy of said at leastluminescent layer is in the range of 75 meV to 200 meV.
 33. Thesemiconductor device as claimed in claim 31, wherein a threshold modegain of each of said at least quantum well is not more than 12 cm⁻¹. 34.The semiconductor device as claimed in claim 31, wherein saidsemiconductor device has a slope efficiency “S” (W/A) which satisfies:S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to said firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well.
 35. The semiconductor device as claimed in claim 34,wherein said semiconductor device has a cavity length “L” of not lessthan 200 micrometers, and each of said first and second reflectances“R₁” and “R₂” is not less than 80% and less than 100%, and said slopeefficiency “S” satisfies S≧1.4/n (W/A).
 36. The semiconductor device asclaimed in claim 31, wherein said semiconductor device has aphoto-luminescence peak wavelength distribution of not more than 40 meV.37. The semiconductor device as claimed in claim 31, wherein saidsemiconductor multi-layer structure comprises a gallium-nitride-basedmulti-layer structure.
 38. The semiconductor device as claimed in claim37, wherein said gallium-nitride-based multi-layer structure extendsover a gallium-nitride-based substrate.
 39. The semiconductor device asclaimed in claim 37, wherein said gallium-nitride-based multi-layerstructure extends over a sapphire is substrate.
 40. The semiconductordevice as claimed in claim 37, wherein said gallium-nitride-basedmulti-layer structure extends over a substrate having a surfacedislocation density of less than 1×10⁸/cm².
 41. A semiconductor devicehaving a semiconductor multi-layer structure which includes at least anactive layer having at least a quantum well, and said active layerfurther including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S≧3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to said firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well, and wherein a standard deviation of a microscopicfluctuation in a band gap energy of said at least luminescent layer isin the range of 75 meV to 200 meV.
 42. The semiconductor device asclaimed in claim 41, wherein a differential gain “dg/dn” of said atleast active layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²). 43.The semiconductor device as claimed in claim 41, wherein saidsemiconductor device has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 44. The semiconductor device asclaimed in claim 41, wherein a threshold mode gain of each of said atleast quantum well is not more than 12 cm⁻¹.
 45. The semiconductordevice as claimed in claim 41, wherein said semiconductor device has acavity length “L” of not less than 200 micrometers, and each of saidfirst and second reflectances “R₁” and “R₂” is not less than 80% andless than 100%, and said slope efficiency “S” satisfies S≧1.4/n (W/A).46. The semiconductor device as claimed in claim 41, wherein saidsemiconductor device has a photo-luminescence peak wavelengthdistribution of not more than 40 meV.
 47. The semiconductor device asclaimed in claim 41, wherein said semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure.
 48. Thesemiconductor device as claimed in claim 47, wherein saidgallium-nitride-based multi-layer structure extends over agallium-nitride-based substrate.
 49. The semiconductor device as claimedin claim 47, wherein said gallium-nitride-based multi-layer structureextends over a sapphire substrate.
 50. The semiconductor device asclaimed in claim 47, wherein said gallium-nitride-based multi-layerstructure extends over a substrate having a surface dislocation densityof less than 1×10⁸/cm².
 51. A semiconductor device having asemiconductor multi-layer structure which includes at least an activelayer having at least a quantum well, and said active layer furtherincluding at least a luminescent layer of In_(x)Al_(y)Ga_(1-x-y)N(0<x<1, 0≦y≦0.2), wherein said semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S≧3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R ₂)}/{(1−{square root}(R ₁ R ₂))×({square root}(R₁)+{square root}(R ₂))}], where “R₁” is a first reflectance of a firstcavity facet, from which a light is emitted, “R₂” is a secondreflectance of a second cavity facet opposite to said first cavityfacet, “α_(m)” is a mirror loss, and “n” is a number of said at leastquantum well, and wherein a differential gain “dg/dn” of said at leastactive layer satisfies 0.5×10⁻²⁰ (m²)≦dg/dn≦0.7×10⁻²⁰ (m²).
 52. Thesemiconductor device as claimed in claim 51, wherein a standarddeviation of a microscopic fluctuation in a band gap energy of said atleast luminescent layer is in the range of 75 meV to 200 meV.
 53. Thesemiconductor device as claimed in claim 51, wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)≦12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 54. The semiconductor device asclaimed in claim 51, wherein a threshold mode gain of each of said atleast quantum well is not more than 12 cm⁻¹.
 55. The semiconductordevice as claimed in claim 51, wherein said semiconductor device has acavity length “L” of not less than 200 micrometers, and each of saidfirst and second reflectances “R₁” and “R₂” is not less than 80% andless than 100%, and said slope efficiency “S” satisfies S≧1.4/n (W/A).56. The semiconductor device as claimed in claim 51, wherein saidsemiconductor device has a photo-luminescence peak wavelengthdistribution of not more than 40 meV.
 57. The semiconductor device asclaimed in claim 51, wherein said semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure.
 58. Thesemiconductor device as claimed in claim 57, wherein saidgallium-nitride-based multi-layer structure extends over agallium-nitride-based substrate.
 59. The semiconductor device as claimedin claim 57, wherein said gallium-nitride-based multi-layer structureextends over a sapphire substrate.
 60. The semiconductor device asclaimed in claim 57, wherein said gallium-nitride-based multi-layerstructure extends over a substrate having a surface dislocation densityof less than 1×10⁸/cm².
 61. A semiconductor device having asemiconductor multi-layer structure which includes at least an activelayer having at least a quantum well, and said active layer furtherincluding at least a luminescent layer of In_(x)Al_(y)Ga_(1-x-y)N(0<x<1, 0≦y≦0.2), wherein a threshold mode gain of each of said at leastquantum well is more than 12 cm⁻¹, and wherein a standard deviation of amicroscopic fluctuation in a band gap energy of said at leastluminescent layer is not more than of 40 meV.
 62. The semiconductordevice as claimed in claim 61, wherein a differential gain “dg/dn” ofsaid at least active layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).
 63. Thesemiconductor device as claimed in claim 61, wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 64. The semiconductor device asclaimed in claim 61, wherein said semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R ₂)}/{(1−{square root}(R ₁ R ₂))×({square root} (R₁)+{square root}(R ₂))}], where “R₁” is a first reflectance of a firstcavity facet, from which a light is emitted, “R₂” is a secondreflectance of a second cavity facet opposite to said first cavityfacet, “α_(m)” is a mirror loss, and “n” is a number of said at leastquantum well.
 65. The semiconductor device as claimed in claim 64,wherein said semiconductor device has a cavity length “L” of not lessthan 1000 micrometers, and said first reflectance “R₁” is not more than20%, said second reflectance “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).
 66. Thesemiconductor device as claimed in claim 61, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 67. The semiconductor device as claimed in claim 61,wherein said semiconductor multi-layer structure comprises agallium-nitride-based multi-layer structure.
 68. The semiconductordevice as claimed in claim 67, wherein said gallium-nitride-basedmulti-layer structure extends over a gallium-nitride-based substrate.69. The semiconductor device as claimed in claim 67, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 70. The semiconductor device as claimed in claim 67, whereinsaid gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².71. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein a threshold mode gainof each of said at least quantum well is more than 12 cm⁻¹, and whereina differential gain “dg/dn” of said at least active layer satisfiesdg/dn≧1.0×10⁻²⁰ (m²).
 72. The semiconductor device as claimed in claim71, wherein a standard deviation of a microscopic fluctuation in a bandgap energy of said at least luminescent layer is not more than of 40meV.
 73. The semiconductor device as claimed in claim 71, wherein saidsemiconductor device has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 74. The semiconductor device asclaimed in claim 71, wherein said semiconductor device has a slopeefficiency “S” (W/A) which satisfies: S<3×{α_(m)/(12×n)}×[{(1−R₁){square root}(R ₂)}/{(1−{square root}(R ₁ R ₂))×({square root} (R₁)+{square root}(R ₂))}], where “R₁” is a first reflectance of a firstcavity facet, from which a light is emitted, “R₂” is a secondreflectance of a second cavity facet opposite to said first cavityfacet, “α_(m)” is a mirror loss, and “n” is a number of said at leastquantum well.
 75. The semiconductor device as claimed in claim 74,wherein said semiconductor device has a cavity length “L” of not lessthan 1000 micrometers, and said first reflectance “R₁” is not more than20%, said second reflectance “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).
 76. Thesemiconductor device as claimed in claim 71, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 77. The semiconductor device as claimed in claim 71,wherein said semiconductor multi-layer structure comprises agallium-nitride-based multi-layer structure.
 78. The semiconductordevice as claimed in claim 77, wherein said gallium-nitride-basedmulti-layer structure extends over a gallium-nitride-based substrate.79. The semiconductor device as claimed in claim 77, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 80. The semiconductor device as claimed in claim 77, whereinsaid gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².81. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well, and wherein a standard deviationof a microscopic fluctuation in a band gap energy of said at leastluminescent layer is not more than of 40 meV.
 82. The semiconductordevice as claimed in claim 81, wherein a differential gain “dg/dn” ofsaid at least active layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).
 83. Thesemiconductor device as claimed in claim 81, wherein a threshold modegain of each of said at least quantum well is more than 12 cm⁻¹.
 84. Thesemiconductor device as claimed in claim 81, wherein said semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to said firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well.
 85. The semiconductor device as claimed in claim 84,wherein said semiconductor device has a cavity length “L” of not lessthan 1000 micrometers, and said first reflectance “R₁” is not more than20%, said second reflectance “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).
 86. Thesemiconductor device as claimed in claim 81, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 87. The semiconductor device as claimed in claim 81,wherein said semiconductor multi-layer structure comprises agallium-nitride-based multi-layer structure.
 88. The semiconductordevice as claimed in claim 87, wherein said gallium-nitride-basedmulti-layer structure extends over a gallium-nitride-based substrate.89. The semiconductor device as claimed in claim 87, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 90. The semiconductor device as claimed in claim 87, whereinsaid gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².91. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well, and wherein a differential gain“dg/dn” of said at least active layer satisfies dg/dn≧1.0×10 ⁻²⁰ (m²).92. The semiconductor device as claimed in claim 91, wherein a standarddeviation of a microscopic fluctuation in a band gap energy of said atleast luminescent layer is not more than of 40 meV.
 93. Thesemiconductor device as claimed in claim 91, wherein a threshold modegain of each of said at least quantum well is more than 12 cm⁻¹.
 94. Thesemiconductor device as claimed in claim 91, wherein said semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to said firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well.
 95. The semiconductor device as claimed in claim 94,wherein said semiconductor device has a cavity length “L” of not lessthan 1000 micrometers, and said first reflectance “R₁” is not more than20%, said second reflectance “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).
 96. Thesemiconductor device as claimed in claim 91, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 97. The semiconductor device as claimed in claim 91,wherein said semiconductor multi-layer structure comprises agallium-nitride-based multi-layer structure.
 98. The semiconductordevice as claimed in claim 97, wherein said gallium-nitride-basedmulti-layer structure extends over a gallium-nitride-based substrate.99. The semiconductor device as claimed in claim 97, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 100. The semiconductor device as claimed in claim 97, whereinsaid gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².101. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}(R ₁ R₂))×({square root}(R ₁)+{square root}(R ₂))}], where “R₁” is a firstreflectance of a first cavity facet, from which a light is emitted, “R₂”is a second reflectance of a second cavity facet opposite to said firstcavity facet, “α_(m)” is a mirror loss, and “n” is a number of said atleast quantum well, and wherein a standard deviation of a microscopicfluctuation in a band gap energy of said at least luminescent layer isnot more than of 40 meV.
 102. The semiconductor device as claimed inclaim 101, wherein a differential gain “dg/dn” of said at least activelayer satisfies dg/dn≧1.0×10⁻²⁰ (m²).
 103. The semiconductor device asclaimed in claim 101, wherein a threshold mode gain of each of said atleast quantum well is more than 12 cm⁻¹.
 104. The semiconductor deviceas claimed in claim 101, wherein said semiconductor device has aninternal loss “α_(i)” (cm⁻¹) which satisfies α_(i)>12×n−α_(m) (cm⁻¹),where “α_(m)” is a mirror loss, and “n” is a number of said at leastquantum well.
 105. The semiconductor device as claimed in claim 101,wherein said semiconductor device has a cavity length “L” of not lessthan 1000 micrometers, and said first reflectance “R₁” is not more than20%, said second reflectance “R₂” is not less than 80% and less than100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).
 106. Thesemiconductor device as claimed in claim 101, wherein said semiconductordevice has a photo-luminescence peak wavelength distribution of not morethan 40 meV.
 107. The semiconductor device as claimed in claim 101,wherein said semiconductor multi-layer structure comprises agallium-nitride-based multi-layer structure.
 108. The semiconductordevice as claimed in claim 107, wherein said gallium-nitride-basedmulti-layer structure extends over a gallium-nitride-based substrate.109. The semiconductor device as claimed in claim 107, wherein saidgallium-nitride-based multi-layer structure extends over a sapphiresubstrate.
 110. The semiconductor device as claimed in claim 107,wherein said gallium-nitride-based multi-layer structure extends over asubstrate having a surface dislocation density of less than 1×10⁸/cm².111. A semiconductor device having a semiconductor multi-layer structurewhich includes at least an active layer having at least a quantum well,and said active layer further including at least a luminescent layer ofIn_(x)Al_(y)Ga_(1-x-y)N (0<x<1, 0≦y≦0.2), wherein said semiconductordevice has a slope efficiency “S” (W/A) which satisfies:S<3×{α_(m)/(12×n)}×[{(1−R ₁){square root}(R ₂)}/{(1−{square root}+ (R ₁R ₂))×({square root}+ (R ₁)+{square root}+ (R ₂))}], where “R₁” is afirst reflectance of a first cavity facet, from which a light isemitted, “R₂” is a second reflectance of a second cavity facet oppositeto said first cavity facet, “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well, and wherein a standard deviationof a microscopic fluctuation in a band gap energy of said at leastluminescent layer is not more than of 40 meV.
 112. The semiconductordevice as claimed in claim 111, wherein a differential gain “dg/dn” ofsaid at least active layer satisfies dg/dn≧1.0×10⁻²⁰ (m²).
 113. Thesemiconductor device as claimed in claim 111, wherein a threshold modegain of each of said at least quantum well is more than 12 cm⁻¹. 114.The semiconductor device as claimed in claim 111, wherein saidsemiconductor device has an internal loss “α_(i)” (cm⁻¹) which satisfiesα_(i)>12×n−α_(m) (cm⁻¹), where “α_(m)” is a mirror loss, and “n” is anumber of said at least quantum well.
 115. The semiconductor device asclaimed in claim 111, wherein said semiconductor device has a cavitylength “L” of not less than 1000 micrometer, and said first reflectance“R₁” is not more than 20%, said second reflectance “R₂” is not less than80% and less than 100%, and said slope efficiency “S” satisfies S<2.1/n(W/A).
 116. The semiconductor device as claimed in claim 111, whereinsaid semiconductor device has a photo-luminescence peak wavelengthdistribution of not more than 40 meV.
 117. The semiconductor device asclaimed in claim 111, wherein said semiconductor multi-layer structurecomprises a gallium-nitride-based multi-layer structure.
 118. Thesemiconductor device as claimed in claim 117, wherein saidgallium-nitride-based multi-layer structure extends over agallium-nitride-based substrate.
 119. The semiconductor device asclaimed in claim 117, wherein said gallium-nitride-based multi-layerstructure extends over a sapphire substrate.
 120. The semiconductordevice as claimed in claim 117, wherein said gallium-nitride-basedmulti-layer structure extends over a substrate having a surfacedislocation density of less than 1×10⁸/cm².